This entire discussion is about feeling valued.
Value comes from scarcity. It happens when you are able to offer something beneficial that many other players cannot. That, unfortunately, requires a skill differential.
There is no intrinsic value in healing something that everyone expects you to be able to heal. Sure, if you don't press the heal button sometime over the course of the next three raidwide casts, everyone dies. But you are expected to be able to heal that. If you fail to do a basic task like that consistently, there are more than enough players who are up to the task and are able to replace you after the team silently disbands. You will not get applause and accolades from your teammates for just doing your job.
There is a gameplay mode where healers are intrinsically the most valuable players on the field, and that's PvP. That's because damage is not scripted, and players know that when you pull off a clutch save on a teammate who is being focused down, you've done something that another healer may not have been able to pull off. You're also everyone's priority target, so you've probably also pulled off said clutch save while kiting circles around their melee.
Healers are also valuable in entry level content. Your team doesn't know what they are doing and everyone dies to a mechanic. But wait! You LB3 and everyone is back up again. Or perhaps you keep the tank alive and the two of you take the boss down from 80% to the clear. Everyone showers accolades on you. It feels great.
This stops working the instant you go near anything with a non-trivial dps check. Which is as it should be. Everyone should carry their weight. But the only things that matter at that stage are pass-fail mechanics which you are expected to perform correctly, and dps.
Historically, the reason why tanks and healers have been okay with this design in harder content is because if you were good, you could become a 'fifth dps' while performing your primary role. So even after you've learnt the pass-fail mechanics, there was still something of value to optimize. There were no clutch saves, but at the end of the day, everyone was blown away by the fact that you put out more damage than the BRD.
It was fun, but the dev team doesn't want this.
So sure, you can be the best player that you can be and put out as much damage as you can while doing the mechanics. But does it really matter? The real heroes are the DPS, because that's where the majority of the raid damage always comes from irrespective of how grossly inept they are. The only thing left for you to do on one of these other 'support' roles is to do your job on pass-fail mechanics. Nobody will value you for when you succeed, but they certainly will chew you out if you fail.
I think that even if you try and reverse this by giving healers more complex dps rotations and giving them a bigger portion of the raid damage pie, you're still at a disadvantage. Every job has an action budget of around 25-30 actions. DPS jobs are always going to have more elaborate rotations than you do because they don't need to budget for nearly the amount of support actions that you do.
The most impactful change that could be made is to re-evaluate how fights are designed in this game. The current standard of completely scripted, choreographed rail-shooter fights has to stop. Damage patterns need to be more complex and less predictable. Fights should deliberately force attrition of your defensive resources and require smart resource management to survive. You need a skill differential that impacts the end outcome.
The problem right now is that healers have nothing of value to contribute. You can only do your job, and that's it. You don't need to be good, most of your team can't tell the difference either way. You just need to exist.