I don't main healer, I main Dancer for the most part. But I do play healers a fair bit when running group content. More often then not I'll run white mage or scholar during a roulette dungeon or trial. When I first heard of this "healer strike", my initial thoughts were "this is stupid, and probably just an excuse to go play the two new classes like they wanted to anyway." And amusingly, no "healer strike" movement seemed to actually kick off in-game. It was almost entirely within this very thread. Still, my thoughts on the supposed issues being complained about...

Tanks and DPS getting self healing is not actually that big of a deal, and doesn't noticeably detract from a healer's role in the group. Said abilities are often on somewhat long cooldowns or are honestly not very helpful. A Gunbreaker's Heal-Over-Time ability is great, for the 15 or so seconds it lasts. But it doesn't keep up with most incoming damage very well. If it is enough healing during a dungeon, then a white mage casting regen at the start of each fight would have had the exact same effect. A warrior has the most impressive self healing capabilities, but those are again on a long enough cooldown that you're not able to use them all the time. And a paladin's healing is too expensive to use all the time. The healing abilities for DPS that I've seen are all ether lackluster or have too long of a cooldown to be viable for doing more then reducing the strain on a healer when things are going south. Maybe there are abilities I haven't gotten to try yet which change the equations, but I'm not seeing any Tank or DPS who don't need healers in group content. At best, most can reduce the strain on the healer when things are going wrong. Maybe the dancer pops Curing Waltz after two rapid aoes decimated the group's HP, thus reducing the healer's work load to recover the party's health from the hits. But is that really a bad thing?

The DPS rotations of healers, yeah those are pretty damn boring. Toss a single target DoT on an enemy, spam the same single target attack. Or spam their one aoe attack spell (if above level 45). It's boring, true. But healers often have limited offensive capabilities in MMOs, that way they can focus more of their attention on supporting the party rather then where they are in their damage rotations. Not sure why anyone would think this design decision is suddenly going to be reversed after all this time either. Healer role is there for Party Support, not DPS. And the bulk of that party support is in the form of healing. If you expect that to suddenly be changed just because a small fraction of the player base gets vocal in the forums, then I feel sorry for you.

At least, that's my opinion.