I created a world without changing any gamerule.Then I find a place and spawn a zombie with its egg.Normally it will pick something following specific rule.Actually,It can’t pick up anything whatever weapon like sword,armour like diamond armour or simple items like glass.I found this error in my survival world.However,in the same world,sometimes zombie could pick up my dropped items.
Not all zombies are able to pick up loot. This is not a bug.