That's the problem in your assumption. The game design gives all DPS a self-heal otherwise they would never get through solo content without the chocobo. Healers get DPS magic otherwise they would have no way to do solo content what-so-ever. In a party environment you're expected to play your role (Tank, Healer, DPS) and trust that the other players will do theirs. If you are healing yourself or other players as DPS and the healer is clearly not in trouble, you're just lowering your DPS contribution. Trust that the healer will do their job, and they will trust you do yours. Your DPS heal will be far weaker than what the healer can do themselves.
That said, in 8-player/24-player content, a red mage or summoner can raise party members faster via vercure (on themselves)+verraise on the KO player targeted which is faster than the AST/SCH/WHM trying to raise without swiftcast.