All mobs can not wield items.

When I use a command such as
summon Zombie ~ ~1 ~ {CustomName:"PrimalSoulX",CustomNameVisible:1,Equipment:[{id:nether_star},{id:leather_boots,tag:{display:}},{id:leather_leggings,tag:{display:}},{id:leather_chestplate,tag:{display:}},{id:skull,Damage:3,tag:{SkullOwner:PrimalSoulX}}]}

It will not hold any item, but will wear all the armour, this happens with natural spawning as well