Steps to Reproduce:

Use either the command /summon piglin_brute ~ ~ ~ {CanPickUpLoot:1b} while in the nether or
/summon piglin_brute ~ ~ ~ {CanPickUpLoot:1b,IsImmuneToZombification:1b} in the overworld or end
Give yourself any non axe item and a golden axe and drop all of them near the piglin brute.
Observed result:
Piglin brutes do not pick up any loot other than a golden axe.
Expected result:

Piglin brutes should pick up any loot and/or equip armor if the NBT tag CanPickUpLoot is set to 1b