If all healing was GCD and all damage was oGCD, all you've done is make me not use any GCDs for minutes at a time and making me wait until I can do a thing that's actually conducive to party success. That doesn't "make me feel like a healer", that just makes me feel like dead weight until the oGCD comes off cooldown.
In order to feel like a healer, there needs to be enough incoming damage to warrant having to spend time healing. At that point, it doesn't matter if you have 50 DPS buttons or 5 DPS buttons, healing will take priority and as such, you would "feel" like a healer even if you only had 2 healing spells.
The feel of a job is about what gets regularly used in a kit, not whether or not it says Spell or Ability. Stormblood really was the high point for healing; enough incoming damage, not too many oGCD heals to replace the GCD heals, and a healthy amount of attack variety when you didn't need to heal (or felt you could risk another hit).
