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For many battles when one side is obviously superior I observe that victors(bad side) almost never finish his enemy.
For instance:
The outcome of battle is similar, weaker side(good one from movies) is defeated but some ship survives(may be heavily damaged but still with life support). Is it part of "Shock and awe" doctrine to leave witnesses of power and break resistance? Or just is it nice for movies?
What are other advantages of not destroying enemy entirely(maybe ambush for rescue)?
On a practical basis, allowing your enemies to surrender has several benefits:
More importantly, however, very few fights are actually that decisive. Unless you can somehow force your opponent into a situation where they can't run away, most battles will end with a retreat and regroup. Once it becomes obvious that you're losing and the chance of victory is very small, the logical strategy is to go somewhere else and try again.
So except in cases where one side has a fixed defensive point (a city or other installation), it's very rare for a situation like you describe to happen.
It's necessary to divide the discussion into two parts: real battles and literary battles. We'll start with real battles.
Other than very small battles (a few dozen or so people) it's essentially impossible to kill everybody on the losing side. Battles are confusing, chaotic events, and spread over a large area. Furthermore, there is typically a wide range of competence among the participants, and a determined, very good combatant (or group of combatants) can generally find a soft spot in the other side. This will allow them to cut their way free. Furthermore, most large military forces contain light, fast units used for reconnaissance, and these scout units are unlikely to take part in the worst of the fighting, and will be well-situated to flee when the battle is lost.
Also, unless the winning side has absolute superiority, they will be unable to completely surround the losers to prevent escapees. To do so invites overwhelming local attacks by the surrounded unit, as the surrounded unit takes on one small part of the other side, defeats it with small losses, and then moves on to the next one. This is called defeat in detail. And if one side does have such overwhelming superiority, the other side will probably do its best to avoid battle in the first place.
Now, as to unreal battles. Umm. It's hard to figure out where to start. Cartoon battles don't have a whole lot of connection to reality, so it's entirely up to the writer to determine what happens. You do realize this, right? In the case of the links you provided, having survivors provides for story continuity, as the survivors go on to avenge the loss. Plus, of course, if the good guys are all killed off in the first scene it's hard to have the rest of the story.
The main advantage of not destroying the enemy utterly is that there generally is no benefit from utter destruction while there is a real cost from committing resources to it.
For example, pursuing fleeing enemies means detaching a force to follow them which means the pursuing force will not be available for anything else. Unless you have an abundance of fast troops, this is usually bad use of resources. Fast troops are generally more useful for screening and reconnaissance and committing them to vanity projects will potentially leave you exposed to enemy stratagems that otherwise would have failed. A policy pursuing fleeing enemies also gives the enemy a trivially exploitable and predictable opportunity to lure the pursuing force into an ambush. Which is even worse use of resources.
Similarly every enemy that flees or surrenders instead of being killed is one less opportunity for your forces to take casualties. Psychologically such "total kill" policy works two ways. It promotes desertion and lack of resistance, which is good and works well for fast campaigns. But if the fighting drags on, the campaign becomes prolonged, you will be fighting enemy that is committed to fighting to the death. This usually translates to high morale for them and high casualties for you. Manuals since ancient times have strongly advised to avoid situations where enemy can't escape for a good reason. So a "total kill" policy should always be targeted on only those cases where either making your potential opponents choose not to fight at all is a priority or you are already fighting fully committed enemies.
Historical examples would be Mongols needing to minimize time consuming siege warfare to fully exploit their superior mobility or religious or ethnic warfare that might already extermination wars, anyway. Asymmetric warfare between superior occupying force and a resistance movement can sometimes devolve into this, if the occupation prioritizes scaring people into not supporting the resistance. But as this causes heavy collateral damage, it is rare unless the occupiers have lot more area under occupation than they can or want to control.Germany had such situation during the World War 2.
One consideration is that the enemy soldiers are also resources with value and dead humans are usually nearly worthless or even have negative value as you need to commit forces to disposing of the bodies. The exception would be if the dead soldiers have value as food or trophies. But generally armies are too large for that value to remain worthwhile if you kill everyone. So this is only realistic for skirmishes or asymmetric warfare where the defeated force is small in relation to the victors.
Generally almost all of the value of the captured soldiers is in their ability to work and they are used as forced labor or sold to slavery. There is also real political value in returning prisoners of war after the war or even exchanging or selling them back during it. This is true even if the "enemy" is supposed to not exist after the war. In that case you have supplanted the enemy and the value of enemy soldiers you did not kill is now your resource. These value considerations do apply to letting fleeing enemies get away, not just on what to do with captured enemies. If your best option is to let them go, why spend resources capturing them?
From the viewpoint of military strategy you should also remember that the goal is usually to destroy the ability of the enemy force to oppose you, not to kill soldiers. As others have noted killing everyone is actually very difficult, so there is almost always several vastly easier methods to achieve your goals without killing everyone. The big exception in history is siege warfare, where you already may have the enemy surrounded and the fighting will likely get ugly and chaotic anyway. In such situations massacres have happened.
I hope this actually contains an answer to the question. In any case it should be useful in giving some context.
In addition to Dan Smolinske's answers, which I think are spot on, leaving witnesses is also an essential part of information warfare. Anyone who has studied war knows that the perceptions of the civilian population is important for ensuring support of the military. Thus, the military provides a great deal of propaganda, which is always one sided.
A survivor can tell a different story, and its hard to argue with an eye-witness. This can soften the resolve of the civilians. It can also soften the resolve of the military, if that individual is returned to duty, but that tends to be more difficult because the military tends to have more resolve to deal with.
However, leaving a survivor leaves a little bit of unknown. The effect of the battle will be more widespread, and less in your control. If you are sufficiently superior, and really just want to finish squashing the worthless vermin so you can get back to your Croquet match, you may be willing to spend more energy to crush the vermin in a way that doesn't depend upon you observing their response to your survivors. If you find the vermin to be so unworthy that you don't even care to win the information game, why leave a survivor, just wipe them out.
Even in real battles where the one side was destroyed to the last man (think of the fate of the Spartan "300" in the battle of Thermopylae, the Texans at the Alamo or the French Foreign Legion troops at Camarón), enough people manage to escape in the confusion to bring the story back to their homes. As well, the victors will probably have a story to tell as well, for propaganda purposes.
While a 100% casualty rate in warfare is very rare (we remember the 300, the Alamo and Camarón because they are unusual events), there are usually enough eye witnesses for both sides, including disengaged forces in the reserve or flanks, Non-combatants who are following the force or even journalists in the modern era, who will be able to piece together at least part of the story. As well, while a defeated force is usually bad for morale, the historical examples ended up stiffening the resolve of the survivors, most of whom took it upon themselves to either avenge the deaths, or become more determined to fight and fight well to prevent such a fate from happening to them as well...
Not really answering the question but many armies try to injure enemy soldiers rather than kill them, on the logic that an wounded soldier takes up more resources than a dead one.
I have heard many cases of attacks designed to demoralize enemy where survivors are left, but for a NATO force it is not currently common practice.
Often desertion from battle was punishable by death. The commanders of the losing side will want to have an ordered retreat, where entire units of troops survive, and will actively work towards that goal when the battle is lost but not yet over. As commander of the winning side you want the enemy to make an ordered surrender or an unordered retreat where people flee disorderly, which makes it much easier to run them down, and the survivors may be unable to rejoin their army without facing severe penalties. In both of these cases you have survivors to spread the word but got rid of the enemy combatants.
Even if you kill all enemies, in battles of tens of thousands it's incredibly likely that some will survive by feigning death and sneaking away in the night.
The times where you'd let entire units flee is if you either cannot stop them easily or with low risk*, if there are diplomatic reasons (sign of goodwill), or you are reasonably certain you won't have to face the troops again. Keep in mind even in the diplomatic case it's often better to capture and disarm the enemy, then release them, instead of just letting them retreat on their own.
*Stopping a retreating unit is hard if the commanders' attention is required in other places. Stopping a retreating unit is high risk if the terrain makes it possible that enemy reinforcements could lie in ambush. It's even harder and riskier if the enemy unit is still in good shape and can defend itself.
In medieval times persons of rank where clearly defined from the rank and file grunt with the idea that you were more valuable alive as a captor than dead (held for ransom). These prisoners were not imprisoned but often were treated accoring to their rank and kept in open custody.
In today's world where snipers abound badges of rank are greatly subdued and hard to distinguish from even moderate distances.
Another item of note was the pardoning of captured enemies with their promise not to fight this was practiced from at least the days of Caesar until the American Civil War.
Current Military Codes (i.e. UCMJ) , specify that an officer cannot accept a pardon but must must continue to fight on.
This verse is about God showing other people why wicked people were destroyed, by allowing them to observe the character of survivors.
Ezekiel 14:23 You will be consoled when you see their conduct and their actions, for you will know that I have done nothing in it without cause, declares the Sovereign LORD." NIV
But, certainly, a more common motive for leaving or releasing survivors is to demoralize rather than "console".
