Sure you can find a few CONs or THMs to heal but lemme find one that doesn't get pigeonholed into it and gets to nuke. Not a single one. Thats a problem with 1. the class, 2. the abilities.
IMO that's a problem with the combat mechanics more than anything. If the game doesn't encourage nuking there's no difference between having a SCH that always heals in a party or having a BLM that never gets to participate in anything.

They could simply make the current nukes stronger and nukers more important- no need to necessarily introduce a "BLM". Both solve the same problem- that nukers aren't currently needed.