One thing to consider is you can always just make damage meaningful. Playing FF6 and FF7 again recently, damage was never meaningful from the enemies. Boss hits my team with an attack, and I just had my "Healer" Curaga the entire party, and I was fine for the cost one party member round making damage not meaningful. Then on the other foot, playing some games like Trails in the Sky/Trails of Cold Steel, some bosses are absolutely relentless. You have your Healer healing, but you're well aware it's not enough in the long run, but you bring two people in to heal and you know you're in for a long fight. The game doesn't have X Potions, and Elixirs common as get out of a bad situation card, so you tend to have to use more creative means to survive. You can spam heal La Tear much like you would spam Curaga in Final Fantasy, but its expensive, and not as efficient as damage has more impact. So you actually have to rely on buffs to reduce the damage you take, and sometimes completely negate a hit on someone to free up your time. Most games, don't make you think like that. You use strong healing items like Elixirs and X Potions, or have someone dropping Curagas all the time, basically invalidating enemy damage.
Anyways, mini-rant aside, instead of limiting the amount of healing you can do, which just feels bad as a player and prevents my favourite "Oh no" moments I've gotten, being I was too defensive and dug myself in to a hole - Just make it so damage is important. If you don't want people to just sit there and spam heal to get themselves out of situations, give them other ways to go about it, and then make enemies change how the player reacts. Light damage? Yeah, Curaga is fine. But heavy, constant damage? Buffs, and other means are likely to take priority in the long run. In the end, I've seen a lot of people like the safety net of a Healer and Healing Abilities, so I wouldn't limit it, or remove it - I'd just alter how the game works around it and don't trap yourself by making X Potions and Elixirs common like I see a lot of RM Games, and even games like Final Fantasy do.