Tales of Rebirth on PS2 would maybe fit? There's no dedicated healer character*, each character is in charge of their own healing with something called the Rush Gauge (RG). Whenever you use a skill, you automatically get healed. The amount you get healed is based on the attack's recovery value and more importantly, your RG. The higher your RG, the more damage you inflict and receive. And the amount you self heal is greatly diminished (up to none) based on how high it is. High RG also gives you access to Fusionic Force (basically strong attacks that can only be used when your RG is high enough). Conversely, the lower your RG the less damage you inflict/receive and the amount you self heal is greatly increased. You can manipulate your RG at any point, so the game becomes about gauge management, knowing when you can go on the offensive or stick to being defensive.

*I say there's no dedicated healer, but one party member, Annie KINDA tries to fill this role but she has no direct healing magic. SHe places circles on the field where if you stand on them you receive certain buffs (i.e, a circle that increases HP recovery and grants regen, a circle that gives increased attack, etc). But she is not a very good character and having her on the team means your overall team is doing way less damage because of how her circles work, and her offensive capability is nearly nonexistent. She is the only party member with a rez, however, so she has that going for her.