[prewett]

Any defenders defending a tower are obviously above the ground floor, which is where access to food and water is. So why bother fighting up the stairway, when you can just block all the downstairs exits? The castle's defenses are the walls; if attackers are in a position to go up the stairs then the castle's defenses have failed, and the only defense left is the manpower of the defenders. So instead of being "besieged" up their towers, the only realistic strategy the defenders have is to come down from the towers and join the melee. Or just surrender, because the attackers have an army and the castles only had dozens of defenders (if that). What tactical situation do you have in mind where the success of the attack depends on success in a staircase battle?

[ramblenode]

Defense in depth isn's about justifying in advance how every measure will win the battle; it's about giving yourself as many small, incremental advantages as possible so that the odds steadily tick up in your favor. Battles are famously difficult to predict so every advantage is sought, and even small advantages can have multiplier effects.

[wongarsu]

Every day the attackers besiege you is one they have to defend against potential counterattacks from your allies. And even if your castle falls you might buy your empire time to raise a bigger army and rally more allies in order to win the next bigger war. Delaying enemies could be an important function of castles.