I like the separate character inventories used in Dragon Quest. A shared inventory is more convenient, but also makes things easy since all characters will have access to every healing item in the game at no cost. Things are lot less tense when the tanky Fighter can just reach into a pocket dimension containing dozens of Phoenix Downs and Megalixers when the Healer goes down.
If players are content to go into the menu to change equipment, change classes/materia, use skills points, etc. then it should be fine to take a few extra seconds to make sure each character is carrying a couple potions. I only see this being a problem when items are an afterthought and not generally worth using except as a do-over button to fix the rare mistake. The more important items are, then the more worth it is becomes to take a moment to think about how to use them.
It makes sense in a game like Dragon Quest due to how the item system and ability system work. Characters don't have that much MP for a long time and MP-restoring items are rare in most DQ games, so using items to heal whenever possible makes a lot of sense. Some items, including equipment, are enchanted and can cast a spell for free which gives the player a reason to hang on to many items all game. The abilities available to a character are also determined by the weapon they have equipped, so characters can change their skillsets/classes by going into their inventory as changing their weapon as a free action. Deciding what items to give a character with limited inventory slots is effectively part of character building. The choice to give a staff that can cast revive to a tanky Soldier that is unlikely to die first, or a speedy Thief that will almost always act first, is a lot like combing class skills in a game like Final Fantasy 5.
There shouldn't be a problem putting limits on the player as long as those limits lead to interesting options. If your game's items are very useful, then players should expect there to be some kind of limit to using them. But it doesn't hurt to design menus to reduce the time it takes to make those choices either.