Next healer class released should be

[RyuDragnier]

I know this would be an unpopular opinion, but I don't think an inventory-based job is the way to go for battles, especially for a healer. Does using potion actually have to be in the inventory, what happens then if you run out, let's say in the middle of an ultimate difficulty duty?

It doesn't have to be inventory based. In FFX-2 the (Al)chemist class could use potions regardless, even if you didn't have them in your inventory. Said skills were called "Stash" skills, and were describe as such by the game's Help description, "Use a hidden item. Takes time, but no item are expended."