My understanding is that Everett has done his best to make a controversy of it, with most linguists preferring to try to ignore him. Unfortunately that's hard when he's doing the Pinker jig, engaging in pop linguistics, etc. So people are forced to engage with it.

I generally agree; finding a language which opts not to use recursion would be a weird phenomenon, and might make certain claims about UG weaker. But it wouldn't invalidate all of traditional linguistic research for the past however many years or totally upend our current theoretical frameworks.