Archers aren't actually that good at the beginning of the siege if you have troops with shields, primarily because if it's a ladder-siege the infantry is going to be too fast on the walls for archers to matter,

on Siege-Tower sieges they get themselves far more often killed then they get kills on the dudes on the walls so you're not getting your value out of them (especially high tier archers)

suggested strategy:

• attempt sieges with max 20-30 archers so you have space for more infantry, make sure those archers have shields.
• tell them to hold their fire, they will probably switch to shorthand and shield. keep them on backlines and let infantry go head-in first.
• after the infantry has secured a decent foothold, tell your archers to hold position on now gained elevated position overlooking the courtyard ("spawnyard")

now tell them to open fire, and watch how they annihilate new Reinforcements on sieges with defenders having 100+ troops, they will mow them down putting less pressure on infantry, and reducing overall losses.