Short answer: No. Why would we do that?
On a personal level, I see Facebook as a useful tool that makes my life appreciably better for many different unrelated reasons, but this question asks about the EA community, so I'll stick to that side of things.
As long as Facebook exists, there will be a lot of people who use it as a primary platform for making plans and hanging out with people, and those people will be less likely to stick with EA if the community mostly disappears from Facebook. (Also, if the "mainstream" groups went down, groups like Dank EA Memes might still up; I don't have any beef with that groups, but it's not the first thing I want a search for "effective altruism" to return on Facebook.)
I've seen squabbles break out on Facebook groups, but those were rarely any worse than the most awkward in-person interactions I've seen in the community; they're also public, and involve people using their real names, which helps to keep things somewhat civil. I'm more uncertain about the EV of small, private EA message groups within Facebook, but I haven't seen evidence that they are actively harmful.
I agree with Zvi that the newsfeed is poorly designed and that some of the company's business practices aren't especially ethical, but I haven't seen it cause any kind of collective harm to the movement, or even to many individuals in the movement.