Every Roulette asking for Healer in Need would like a word with you about that. By just reducing healer DPS to three buttons, healers have become less popular than tanks. Should this linger beyond the initial hype, this will be the first time in over half a decade tanks are no longer the role in constant demand. And you somehow surmise locking out DPS completely in Duty content would bring in more healers? No. It would all but guarantee a mass exodus, and the new meta for Savage content to include five DPS and only one healer.
... Raw went from a Parry bonus to a flat 25% defensive ability on a 25 second cooldown. That is leaps and bounds superior in every facet. It sharing a CD with Nascent Flash matters little because they have different uses. The latter is intended for use while OTing—essentially providing Warrior with a TBN/Intervention equivalent. Raw is for when you're MTing. Speaking of TBN, an additional 5% of a tank's HP is much more potent. We're boasting six digits now. That is no small amount.
Old Raw was on a 90s CD compared to 25s now. That is almost four times the usage for a CD you acknowledges is stronger. Seriously. And what? Warrior was more tanky before? They didn't even have a tank stance. Defiance only boosted their HP. Warrior literally got a 20% free defensive buff. While DRK did lose some of its HP sustain, you typically wanted to avoid Dark Arts Abyssal Drain because it was technically a DPS loss unless you were overcapping on MP.
As for Protect. The mitigation of it was so low, you often wouldn't even save a healing cast if memory serves. It had a purpose much in the same way food or materia does but it wasn't anything significant. Furthermore, tank stats as a whole accommodate some losses. Hence why tanks are often taking less damage now than during Stormblood's release. You have to consider prior to 5.0 tanks did not have a 25s 20% CD they essentially spam. That contributes significantly more than Protect ever did.