Semi-Hidden Witch Mechanic: Inventory

Villagers have a hidden inventory that can hold a few items. What if Witches had a hidden inventory that could only hold potions? My idea is that when you drop a potion of any kind near a witch, it will pick it up and add it to its inventory. If it is a standard potion with a positive effect, the witch will drink it when fighting a player. If it is a splash or lingering potion, then the witch will throw harmful potions at players and villagers, and throw useful potions at Illagers and undead mobs.