why every FF14 healer is berserk healer

[Shurrikhan]

They say they only want to heal, but they're also the first to crumble on the rare occasions where an XIV fight becomes more healing intensive than the single raid wide every 30+ seconds, which is still a long way away from the constant pressure of attrition healing that WoW had for a very long time.

Yeah... I have to hugely doubt anyone who fits that bill would be coming from WoW over the "exodus" period, where Heroic/Mythic raids wiped if healers couldn't simultaneously keep up with burst, sustain, and sometimes damage, generally with considerably more elaborate setup required for said burst healing rather than just hitting oGCDs on castbar / Simon Says cues.

the most well known game with this type of healing.

It may be well known, but from all I've seen of both average and upper-end play, its type of healing generally fits your description far less than the other examples provided, be that in WotLK heroics if going with any decent speed, to Cata Heroics and raids to MoP's, to WoD's, to especially Legion's, BfA M+ and certain raids, and later Shadowlands. DF and TWW have been a bit less rewarding of 'downtime' tasks but still enough to keep them plenty obligatory.

..."healers only heal" and "princess healer"-types.
When you mention that phrase it usually implies a specific playstyle.

It does, but enough to make me think they almost certainly hadn't survived WoW, where they'd have been expected to weave in CC, add focus damage where possible, potentially actively set up for burst, manage a DPS rotation, possibly track DPS charts and CDs for durationed external buffs (Seasons, Infusion, etc.), bank particular CDs for particular trash pulls, etc.

I would trust a "princess healer" far, far more here in XIV than in WoW. Still little, but WoW's context would be even more condemning.

Rather, if I wanted to ensure fewer "princess healers"... I'd try to have our healing be more like that of Shadowlands or Dragonflight-era M+ or Heroic Raids, just with less neutered damage (e.g., nearer to Legion's).

...Sadly, instead, WoW: Midnight is going the way of Dawntrail instead. (Or worse, really, especially by contrast to where it is now and had been going before this upcoming massive jump towards simplification / mobile-game level kits.)