Oddly enough, some of the better healing experiences I've had were in games are where damage is 100% avoidable. But the key difference is they're harder to predict; not on set timelines, etc.
You touch on this when you comment dodging is easy for veterans. Even in a fight like Z extreme, you're often looking to see if the safe spot is in one of two locations (Slightly more for the stars, but there will always be a safe spot in the front half of the arena). The fights rigidly conform to patterns, have set timelines where there might be 2 paths or maybe you don't know if the mechanic will be "in" or "out" but it always occurs at the same time so you're ready for both.
A game that's as set or predictable as FF14, then, runs into several problems. At least in harder content or content meant to present a challenge... Even messing up once has to often be lethal (or in the case of ultimates and harder savages, a group wipe event). A lot of damage has to be unavoidable, but not too much so a healer death can be recoverable at least a little bit of the time.
But even if you do all that, the whole GCD uptime design means there's a lot of healing/recovery downtime. And thus... we run into the stale healer problem, not limited to ex primals but even extending up into ultimates.