I agree with OP but this all really started being a problem in Stormblood. Back in HW/ARR encounter design was pretty much the same as it is now, but healing felt more engaging by several orders of magnitude. This is cuz healers design was changed but encounter design did not.
- In ARR and HW healers had more complex dps rotations (even AST's barebones rotation got even more barebones in stormblood when we lost combust ii as an extra, casted dot).
- Dpsing as a healer carried a risk because of Cleric Stance, even if it was a mostly subjective risk (once you learn a fight there was virtually no risk of using CS). People were more understanding of less experienced healers not dpsing because of this perceived risk. Regardless of experience or the encounter's difficulty, cleric stance added an actual decision making factor into healing even when doing casual content. With it gone healer dps got even easier.
-There were way less ogcd healing skills, which meant all healers had to cast gcd heals a lot more often, despite the encounter design being the same as it is today. WHM had pretty much the same skills bar lilies. SCH only had lustrate, indom and whispering dawn. AST only had CU and ED.
- Precasting heals for incoming damage, be it tankbusters or raidwide aoe, was an actual skill you had to have as a healer. Not in all content and for all damage, but without so many ogcds to supplement gcd healing, it was possible to not have enough time to top everyone off for the next mechanic if damage was frequent and you were healing reactively (i sure remember a12s almost holies...).
Now even in ultimates we just spam the same dps button, wait for damage to go off, press an ogcd heal, and keep spamming the same button. Healing as a healer also got a lot easier and mindless.
So in the end, i agree that there is a problem with encounter design, but its moreso a healer design problem. We used to have more to do during downtime, and we also had less downtime. They made healers jobs easier, healing and dps, without giving any complexity back in return. As expansions continue and healer dps gets even more dumbed down and they get even more superfluous healing tools this problem is going to worsen. Encounters would need to do ridiculous amount of continuous, unpredictable damage for us to cast heals even half as much as we did in the past.
I think what i miss the most from old healing was cleric stance just cuz it made optimizing fights and squeezing dps more engaging. Even running stuff like dungeons was not completely brainless like it is now just because you had to actually pay attention of when you were healing the tank, rather than weaving heals into dps spells, but i dont think theyre ever going to add anything that looks remotely similar to it again.