I think in principle the idea works, in practice, rarely so much. It's a variation on "speak with your wallet", which is typically how consumers will deal with stuff they're not happy with and when what they're not happy with affects the company or business they're dealing with then they pay attention. For example, EA and Battlefield 2. In their case, there was enough of an outcry they realised it'd affect them financially and tried to salvage the launch by removing some of their BS.
I think this however, is a little different and if I'm being honest, I'm not sure if enough people would get on board for such at thing for it to matter, because you'd need a lot of people to begin and a lot of people who are disgruntled are probably still gonna play their healer job. It's no skin off my nose, because I'm healing less anyway, because I no longer enjoying the role and I also have a tank levelled and I main a DPS now. People will want to do the new Nier raid and will likely pick the job they're comfortable with. Heck the other thing to bear in mind that not everybody agrees with us that healers are in a bad place, which I think would hinder any effectiveness, because they're unlikely to join in.
But I share the annoyance and frustration that these complaints have been persistent since before Shadowbringers, worsened by Shadowbringers and we've yet to see acknowledgment. Acknowledgement could even be "we don't agree there's a problem, we're going to stick to this", because I'll know then to then not both in gearing my healing jobs and put more attention into my tank and DPS jobs. I'll probably still complain because I'm a healer at heart, but at least we'd know where we stand and can't fault SE's lack of communication and we'd know what we can address or what compromises in design we'd give as feedback.
Heck a "we're looking at it" or "we're reviewing it" would at least give -something- to show there is some level of intent. When the dev team shows good communication on other jobs, even in saying "we don't think there's a problem" (see 3.0 and 4.0 MCH) and when they agree there's a problem, they show intent to do something about it, when there is barely a peep it is easy to find that concerning.