Has anyone quit healing?

[Irenia]

While I'm not for full time healing as a solution, just one correction: full time healing does not equal full time maximum output.
In other games where healing was a full time job you did not have to use your most expensive heals and opted for more efficient ways to conserve resources so you always had ways to heal through unexpectedly high dmg. It was just possible that if the party continued to screw up you may find yourself out of resources. The higher healing requirement of fails was always managable just not for an unlimited amount of time.
Your hardcast toolkit offered enough options and synergies to nicely deal with consistent, average damage and some damage spikes while cooldowns were either used if things got out of hand (with randoms/ in casual content) or strictly planned to meet healing checks (in endgame).

But you'd have to fundamentally redesign the toolkits and encounters to make such a thing possible and FFXIV went the green DPS route.
Might aswell improve on that concept and keep the current healing skill floor while raising the healing + optimized dps skill ceiling through more interesting dps options.

The only problem with this is what does it mean to overgear and overskill content. That is, take a healer that is not ready to take on Savage, but is able to get through an expert dungeon with zero deaths with a party that makes no mistakes in regards to mechanics. Replace that healer with one that clears Ultimate content.

How does the run change?
Do the party feel that the run is improved?
Does the Savage healer feel that their skill makes a difference in this easier content?

I might have missed something, but it seems like there might be a hard skill cieling, where for a given piece of content, better skill and gear only allows you to carry worse players through content, if you were able to get through it before.

[Rilifane]

The only problem with this is what does it mean to overgear and overskill content. That is, take a healer that is not ready to take on Savage, but is able to get through an expert dungeon with zero deaths with a party that makes no mistakes in regards to mechanics. Replace that healer with one that clears Ultimate content.

How does the run change?
Do the party feel that the run is improved?
Does the Savage healer feel that their skill makes a difference in this easier content?

I might have missed something, but it seems like there might be a hard skill cieling, where for a given piece of content, better skill and gear only allows you to carry worse players through content, if you were able to get through it before.

There always is.
If someone outgears content, they will be able to carry weaker players.
If someone outskills content, they will be able to carry weaker players.
At some point, content is simply 'beneath' you in terms of both gear and skill. It doesn't matter wether you have healing as a full time job or a mix of dpsing and healing. If you have good gear and skill you will steamroll casual content. And as all healers must have some sort of dps skills, even with the full time healer design people will eventually switch to dpsing more. It's bound to happen.
Do you feel the difference? You should be able to answer that. Have you never noticed how much faster big pulls meld if the healer is able to go all-out with dps? The difference between a careful zero dps healer and someone who maximizes uptime without endangering the party is huge and noticable for both the player and the party.
That doesn't change with healer design, a dpsing healer will always fasten the run.
But you will obviously reach the skill ceiling at some point. A 'hard cap' is what a skill ceiling is. At some point, there's nothing more you can do. But you're mistaken if you think you've reached the skill ceiling for a full time healer of you managed to keep everyone alive.
Even in games where healing was a full time job, you had things to do during downtime. Be it support or dps. The classes were usually designed with with support and dps abilities from the start (you can hardly heal mobs to death while leveling) but because of the healing > support > dps priority, you simply didn't have the time at first when lacking gear/ practice to make much use of it while as you got better, you started to utilize it more.
And that's not even counting in trade-off mechanics that were also part of this design which let you chose wether to use a spell offensively or defensively.
But as I already said (and you seemed to have missed?): I'm not for full time healers anyway. Not in this game.