In a relatively casual Static, where we didn't really ever get serious enough for an explicit mitigation plan or timeline, but did at least have people using addle/feint/reprisal/etc, for Pandaemonium Savage there were definitely moments in the latter floors of each tier that did feel like they stretched the healing resources and required you to be on your toes and rotate your healing cooldowns. Curtain Call, Purgation, Natural Alignment, High Concept, Harrowing Hell, Superchain and Pangenesis are all mechanics where it felt pretty necessary to GCD heal to not have everyone die. I'm sure with better planning and coordination, you could do it with no GCDs, or one healer or etc, but at the level of "knowing the fight, but not knowing everything every party member will do" level, you're going to have to use your buttons and space out your cooldowns and etc. Which I think seems right for Savage difficulty.
It's important to note that in all those cases it's almost exclusively group healing resources that are being taxed due to significant raid wide damage. Healers also have a lot of single target healing/mitigation buttons and those are almost never needed. The only times I can really remember it being a case of "use single target ability on a target or they die" was the Natural Alignment players in P8S, the Ifrit players in High Concept, and the main tank when doing Lazy Lasers in P12S to absorb the first auto after their invuln falls off. And of course trying to save someone if they messed up a mechanic. I could throw Terachole or Haima on a tank when they were taking a Tankbuster and it'd keep their health comfier, but they could also easily survive it themselves in most cases. I'm sure if you look at my FFLogs for most fights, my single target cooldowns are all massively underused.
Also, for my experience above this was doing final floors after many weeks of gear, so Week 1 groups will be taxed pretty heavily and probably require all the mentioned mitigations to survive stuff. Which also seems correct for people that want that week 1 challenge.
So I think if they amped up more single target damage to tanks, or added more unavoidable damage to specific non-tank players that you had to help survive, that'd be a big help in utilizing the full breadth of a healer's kit.