"I was uncomfortable with how he played because he has a history of cheating so I quit"
Which is entirely reasonable, if you think that cheating is an "existential threat" to chess itself.
If he wants to follow through on this, we better see some damning evidence. If this entire hubbub was for nothing, the chess community as a whole is going to have egg on their face.
Perhaps a person knows they should have done more sooner, but still chooses to do what they think is right when they make a decision.
Who are all the other cheaters that Magnus has quit against?
Why is the only cheater he has publicly made a show of having a problem with in all these years the one who recently beat him OTB playing black?
"His over the board progress has been unusual, and throughout our game in the Sinquefield Cup I had the impression that he wasn't tense or even fully concentrating on the game in critical positions, while outplaying me as black in a way I think only a handful of players can do."
This isn't just "I got weird vibes" or something, this is the professional analysis of someone who has spent a lifetime analysing particular board states, the overall flow of the game, and the psychology of his opponents. He may have his hands tied in terms of what exactly he can say at this time, but the telegraph here is that he suspects cheating because of specific, observable factors in how the prior game(s) went down.
And those factors may ultimately be too subtle to be judged by anyone other than a jury of other top-tier professional chess players, but ultimately that doesn't matter, if it's enough to trigger a more thorough investigation then concrete evidence will emerge one way or the other and show Carlsen to be right or wrong on his hunch.
As much as TV would make you think so that's mostly a myth. It was probably more so the case in the past but now it's at most a very minor part of the game, and most (typically all) of your edge comes from better card playing.
A huge river bluff is viewed in the lens of 'I've represented a range which includes strong hands, and I make money if I get a fold X% of the time while increasing the call chance by Y% when I do have a good hand in this spot' and not 'I'm going to unnerve him by throwing money to make a bad decision'.
Tennis players and Chess players are expected to be granted absolute silence.
Is that an inconsistency? I don't think so. It's part of the expectation of the sport. Sport is in general a weird type of impure competition. Sponsorships, TV contracts, etc, all contribute to mixed priorities.
So no, I don't think it's appropriate to equate Poker and Chess in this regard. Their best practices can be evaluated on their own measures.
Hans claimed he studied against Magnus' opening because Magnus had played it a few months ago. It turns out Magnus has never used that opening in a recorded game. The dialog has now changed to "well by move 20 the board state became identical to a previous Magnus game" but Hans didn't say he spotted the similarities at move 20, he said he studied that specific opening.
You think the players being uncertain whether or not their opponent is cheating is a good thing for chess? The game would crumble.