You want your enemy to try storming your very strong castle even if it is not strategically placed, or at least you need to gain something by building that huge and strong fortress.
But castles are not only useful for this. First, understand your super strong castle controls your territory. Your enemy may destroy whatever it likes and plunder every village on the way to your castle.... yet, the territory will not belong to him while there is that super strong fortress and its garrison inside it. His peasants will never have the opportunity to harvest the land, his merchants will never travel safely, nor would he be able to exploit mines, forests, or rivers in the region. Basically, while your super fortress is still standing, the game is not over for you, and this war brings almost nothing for the attacker, expect wasting his time and gold.
That's why castles were useful even for the small nobility, willing to protect their independence from their peers. Without enough forces to besiege that castle, and hold the land, and protect his own land, no other lord would dare attacking you, because if he did so, he would lose a lot of men and money just to take your land. Making him quite weaker indeed. Probably weak enough to become a prey for small neighbours willing to take the lion's share.
Modern video games do quite a good job to show it. I'm thinking of the Total War and Crusader Kings series. It is easily seen in game, that even a small enemy can be a tough nut to crack when he has a strong fortification. Of course, you can ignore his army and plunder his land. Of course, you can besiege it for years and lose men by hundreds before taking that tiny city. But if you ignore it, then one day his army will come out of the castle, and attack your own village. It will not defeat you, but if you are at war with someone else, you will lose a lot of time, and an important part of your economy. If you besiege it, you will lose a lot of time and perhaps a lot of men. You could even end up in another war, because your neighbours can see you lost troops and are now quite weaker.
In such games, without strong fortifications, the small country's army could just be crushed in an open ground battle, with much less losses, while grabbing the land easily.
That's the point of view of the tactician. Now on a much larger scale, if you don't limit your view to your own castle and to a small war, having such a stronghold is a big thorn in the toe for any invader. Your stronghold, if not taken care of, can:
- Disturb supply lines
- Disturb communications
- Conduct guerilla warfare, while benefiting from an unassailable lair to rest and rearm
- Secure some critical resources
- Act as a strong bridgehead for any future counter attack
- Secure the flanks of any allied army
- Act as a supply depot for any allied army
And so on.
If taken care of by your enemy, then your stronghold still grants benefits in a campaign by :
- Tying down enemy forces, much more forces than what's needed to protect your stronghold
- Gaining time, because such forces will need an invasion force to plan what to do, to split up forces, organize a good siege before leaving. Or else, we're back to "Your stronghold is not taken care of" if the invader does not set a good besieging force.
- Win the economic war. Your castle is a strong asset, it took years to build and cost a lot, but will last for tens of years. When the war breaks out, you most likely have to spend very few bucks on your castle. However, your enemy must still spend money for all these men besieging you. Each passing day, he loses money. Each day that passes, your castle is more and more profitable. In the middle ages, a professional force cost a lot to maintain, good weaponry is incredibly costly, especially for good steel, and these men aren't going to fight for free.
- Decreasing efficiency of the enemy's chain of command. Your stronghold doesn't need many qualified men to hold its ground. Mere sergeants are enough to motivate the troops, even though qualified officer might help. However, besieging a fortress requires at least one or many experienced siege engineers and/or officers to know how to set up the forces, prepare for sorties, prepare their positions in case an external army come to break the siege and so on. In your case, your castle is already built, and it was built by the very same qualified people your enemy now needs to besiege it. You have these qualified people at your disposal to do whatever you want, while your enemy must leave irreplaceable assets behind.
- Your strong castle might be one out of a strong network of castles, forcing your enemy to leave one castle at a time a small force to besiege it, weakening slowly its army. Should your own fortress be too weak, your enemy could storm it immediately. Here, having an impregnable castle is important.
I hope it will help you. Just remember though, do not fall for the classical Maginot trap : your stronghold will never be invincible, and an enemy might still want to avoid it, even though it means all the points we saw earlier. Thus you must take that into account, and perhaps even build your own strategy around it. A strong enough fortress might deter anyone to attack you, deflecting any invader to a less protected region.
That's what some modern days fortress were meant to be in Belgium, France, or even Switzerland, and some did their job well. Maybe that's what you truly need.