Steps to reproduce

1. Make a 1x1 enclosure with a dispenser facing into it on one side.
2. Spawn a skeleton.
3. Confirm that the skeleton cannot pick up items by dropping a sword on it. If it picks up and equips the sword, kill it and go back to step 2.
4. Pick up the sword.
5. Disarm the skeleton using /replaceitem entity @e[type = skeleton] slot.weapon.mainhand 0 air
6. Put a bow in the dispenser.
7. Activate the dispenser with a redstone signal.

Expected result

The dispenser equips the skeleton with the bow.

Observed result

The dispenser shoots out the bow and it floats on the ground.

Unarmed Skeleton (In Creative Mode) can pick up swords and even sometimes axes, but they DO NOT pick up any given bow, either enchanted or not. It doesn't matter if the bow is dispensed or dropped.