Back to the OP’s point:
From my understanding of premodern warfare, discipline is critical. The goal of an army or soldier is not to kill every last one of the other side. Rather, it is to convince the other side that it’s not worth risking their life to defeat you. Which usually means fighting until the other side runs away. (There’s a somewhat famous quote that makes this point more effectively but I can’t seem to find it…)
Most premodern societies, particularly the medieval-ish societies in ASOIAF, don’t have the resources to maintain a large professional standing army. Rather, when they need an army, they conscript as many laborers and farmers as they can spare, and give them weapons and some brief training. Maybe they can field a few regiments of veterans with some experience and training from the last war. Mercenaries will be very experienced but really uninterested in dying for your cause. The core of a feudal army are knights, which are nobles rich enough to buy good equipment and spend most of their time training.
So you have one regiment of conscripts fighting another. Neither are particularly well experienced or trained, or really all that interested in dying for their cause. They fight until maybe 10% of one side are dead and wounded. The losing formation “breaks” because of the gaps left by casualties, and because the remaining conscripts are shocked to see their buddy die. A few run away or stop fighting, the formation continues to break apart, and eventually the losing side is a panicked rabble facing an enemy that can still effectively fight.
Strength is useful, but not critical. Most of your conscripts are merely the least diseased and malnourished peasants. Knights are pretty damn strong and well-trained, but depending on the culture, they might be really effective in single combat but less effective fighting in formations. Any physiological loss of strength caused by castration can be more than made up for with training to improve strength and discipline.
The reason the Unsullied are (in the books) so unstoppable is because they are trained and disciplined. Against a poorly trained opponent, they will take barely any casualties, and quickly kill enough of the other side to break them. Against a better trained opponent, the Unsullied will give and take casualties, but they’ll hold formation and keep fighting until the other side breaks. To defeat the Unsullied you’ll either need similarly high quality soldiers (perhaps your warrior nobles fight in formation), a much larger number of conscripts, or brilliant tactics.
My WAG is that the castration/emasculation is more useful during early training (and brainwashing). Testosterone-filled teenage boys are going to be hard to train to fight as a disciplined unit. They’ll generally act like any other group of idiot teenage boys, discover this “sex” thing might be worth running away and living for, etc.
The disciplined, methodical sacking of a city is just a bonus: rather than raping and looting, the Unsullied could focus on pursuing any surviving enemy.
tl;dr: Unsullied are brainwashed murder robots that keep fighting until the other side runs away.