Skeletons are able to pick up swords / armor in 1.15.2 through dispenser or by dropping the item on the floor but it doesn't work with enchanted bows.
In the latest snapshot (20w14a), no mob is able to pick up items (in my testings though, in creative with spawn eggs and with natural generation during night time).
Apparently, after reading a similar bug report it works using commands, but not without. I believe it's a vanilla feature so it's a bug I guess.
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is duplicated by 1
Comments 4
Also effects Skeletons in 1.16 RC 1. Skeletons on hard will pick up and wear better armor, but never a better bow.
I am unable to reproduce this issue in 20w51a. I've provided the steps I used to reproduce this issue.
/summon skeleton ~ ~ ~ {HandItems:[{id:"minecraft:bow",Count:1b}],CanPickUpLoot:1b}
/give @p bow{Enchantments:[{id:"power",lvl:2}]}I then threw the bow to the skeleton and the skeleton picked it up without any issues.
Tested in snapshot 20w17a, though the problem presents a little differently than how you describe. On normal difficulty setting, I can't get skeletons or zombies to pick up anything at all, be it armor or weapons. On Hard difficulty they pick up armor and weapons just as frequently as usual, but on Normal difficulty I can spawn hundreds of them and none of them will pick anything up.