I've been thinking about this alot, and the short of it is... SE designed themselves into a corner. It was minor in ARR, but it has been getting worse since then.

Given:
1) In FFXIVs culture the minimum to be a 'good' in a piece of content is to never let anyone die, and to not die yourself. If people keep dying then someone is not up to snuff and players feel like they are 'carrying' someone.
2) The only measure of skill and gear in this game that isn't pass/fail is damage dealt. (To qualify, you must be able to 'win more' and have it matter in some way if you play better or get better gear).
3) SE does not want to promote healer DPS, even though it is inevitable due to SE also not wanting every mistake to be fatal.

As long as all three of these things are true, healers will be in a bad spot. If one is false, then things get interesting.

If 1) is false, then you can let people die and still be a good healer, which allows space for mastery beyond just being good. If you enjoy healing 24 man content, it is probably this you enjoy, since it generally is really hard to get salty if one person of 24 dies repeatedly.
There are people for wish that 3) was false. If square embraced the Green DPS idea we'd be getting more interesting skills - they'd all be focused on creating opportunities to DPS more, though.
Making 2) false is ideal, but also difficult. Very difficult. I'm not going to say it is impossible, just that I haven't thought of anything due to the only way the game scores a party in any granular fashion is the elapsed time. Which ties into DPS. You can ignore 2), which is the realm of not only 0DPS healer and the like, since they only care about being "good Enough'.

I truly want to be wrong, but... I dunno.