The fundamental asummetry at play here is that cheating is a lot easier than detecting cheaters in modern chess. As such, I'm not sure insisting on people shutting up unless they can provide ironclad evidence won't just lead to professional chess becoming rife with cheaters (which is presumably the "existential threat" to proffessional chess that Carlsen reffers to in his statement).

I admit that it is a trickly problem, and I agree that Carlsen's behavior here is not beyond reproach. Withdrawing from the tournament only after having lost a game makes the statement much less impactfull since one can not discount the possibility that he's just being a rather sore looser. I would personally have respected his decision much more if he had followed his impulse (again, referred to in his statement) to withdraw as soon as Niemann had been invited to the tournament in the first place.