The issue lies not in the role, but in the game design - again, healers are fine as they are, but the game simply does not challenge the role enough because of how the raid mentality works.
Fights in XIV are designed after a puzzle solution kind of mechanic: There's a win condition; if the win condition is met, mild to no damage is taken by the party. If the condition isn't met, high, possibly unmitigable damage is taken by the party. Whenever such mechanic happens, the boss then uses either a body check mechanic or an incidental heal check mechanic - AoE damage or some generic debuff/buff count - that might result in a wipe depending on the win condition having been met or not. Usually, healers might be able to save a party by using their kit accordingly in the former situation (AoE damage after mechanic) under certain circumstances and power levels.
There are little to no actual heal check mechanics in this game that are heal checks by design. A few examples of that I have in mind are Living Liquid's Splash -> Cascade scenario, TEA's J-Wave enrage or any Savage+ Akh Morn instance in the game, really. These mechanics have but one solution: to mitigate and heal through it. More mechanics like that might help healers fill their uptimes with GCD heals, but is that really desirable? Is that actually good encounter design? I, for one, don't think so.
Saturating a fight with plain AoE damage won't make it harder, just annoying. It's simply forcing healers to press AoE heals just for the sake of it.
Then again, we have another problem: most tank busters in this game allow for invulnerability cheesing. They have been trying to solve that with stackable bleedings and similar solutions, but that also displaces Invulnerabilities. For example, in P8S, invulns are not necessary in any moment during the first phase of the fight, mainly because the boss doesn't allow for their usage in Tank Busters - so they're just left there to be used to correct a mistake if possible.
Invulnerabilities should be made necessary for certain mechanics, not just a smart solution. That would make tank busters a healer-tank team solution rather than just placing it on the shoulders of a single party.
One fight with good healer encounter design that could be taken as an example is The Omega Protocol's Phase 01. Healers have to discuss their healing priority and keep individual members alive throughout the phase with constant damage instances while also solving their part of the mechanic, not excluded from the rest. That, along with some O4S phase two healer-conditional mechanics and Debuff removal mechanics (!! really important, barely used) such as in TEA's Phase 01 and healers will actually have active challenges.