While I also have a preference for which healer to play, the lack of identity and distinct gameplay shows in how easily you can pick up any healer and perform well on it if you've gotten the basics of playing a healer well down like avoiding GCD heals unless a life depends on it, spreading out resources, letting regens do the work etc.

All 4 healers have skills you can easily use in place of something the others have and barely notice a difference, if any. It requires content to really push your toolkit to notice the small differences and that's something that generally only happens in early tier clears of the upper floors and Ultimates.
How often does anyone consciously pair Fey Illumination with Pneuma to mitigate first and get a stronger heal afterwards? How often does anyone consciously use the heal buff from Asylum or Physis II to better spread resources or snapshot stronger Seraph shields? How often is the CU mitigation vital and is not just used as another generic regen? How often does it matter whether you use COpp or Star to heal? The differences are there in theory but one of the things that shows a lack of identity and disctinct gameplay is the lack of difference they make in practice barring extremely challenging content with two healers that really want to push their dps.

And let's not even start with 1 dot, 1 filler and that one extra dps button on a cooldown/ on charges that's the same across all healers.