Because Meat can improvise
Think about Apollo 13. The spacecrafts electrical power system was completely crippled, and with no power to the nav computers was a dead ship. However, Apollo 13 had backup computers running on an auxilary power system - By which I mean a human crew that eats food. The ship might have been dead but the crew was alive, kicking, and highly motivated to get home.
There's also the lesser known case of Apollo 11, where one of the lunar landers electrical switches was damaged. Without that switch, the Ascent engine could not fire, and the LEM would be stuck on the surface. Again, meat saved the day - by jamming the metal tip of a pin into the broken switch, and completing the circuit.
So, while your alien crew might be in a reactor-dead ship, its engineers will still be alive and breathing, working tirelessly to get it back online. Which brings me to another point.
It probably won't be a fight to the death
On the ocean, you don't need to sink a ship to remove it from the fight. Consider the battle between the HMS Hood and the Bismarck, or more importantly their supporting ships the HMS Prince of Wales and Prinz Eugen. During the battle, the Prince of Wales took severe damage and suffered multiple turret malfunctions, forcing her to retreat. Even though it wasn't destroyed, it was effectively no longer a factor for months after.
In fact, destroying the HMS Hood is probably what led to the Bismarcks own destruction - The entire royal navy dropped what it was doing to avenge the Hood. Had the hood been mauled and retreated, there wouldn't have been the same bloodlust to find the Bismarck.
Now consider the USS Cole. A single powerful, point-blank bomb blast crippled all of the ships systems, and was so extensively damaged it needed to be hauled home by a salvage vessel. Were it a battle, sinking the Cole would've been a waste of time and ammunition.
So, like the title says, it won't be a fight to the death. To win a battle you just have to smack your enemy around until they either run away or stop moving. Also, if you're in an FTL setting and don't want to have some kind of warp-disruptor, there's very little you can do to keep the enemy from running away when things go south.
Between Meats ability to improvise and the reality that you don't need to atomize your enemy to get rid of them, it makes sense to have a crewed vessel.