This isn't WoW. You don't have people constantly and randomly getting chunked for 60% of their HP and threatening death if you don't twitch-react to them. Feel free to take it up with the devs, but the running trend for many years now is that damage in Final Fantasy XIV is very, very predictable and on a literal timeline.
Any time healing isn't needed and you're not DPSing, you're not doing anything. If you're not doing anything, you are disrespecting your teammates. Watching health bars like a hawk just means you don't know the fight. Simple as. Get better at playing a healer and you'll realize why it's interminably boring. Just because it's "stressful" when you're worrying about completely imaginary instances of damage that aren't happening doesn't mean it's fine for moderately experienced healers to be mashing one button for the vast majority of a Savage encounter.
What you're proposing is that the healer role should be completely occupied by bad players, and anyone who's remotely good at the game should "graduate" from the baby role. Well, that's already happening. But it completely contradicts your ego about being "the reason everyone is alive." You can't brag about being the thing that holds a party together when you're also advocating that your role be the tutorial role for people who haven't figured out how to use both of their hands at the same time.