Why not just let him play and run analyses on the moves? Surely they can, for example, input all the moves into known chess engines and see if there's a match with the alledged cheater's moves. Then the match will be annulled and the guy ousted.
It's much harder than it sounds. Firstly a top level player will match the top engine move 65+% of the time when playing legit, so it isn't that unusual to have a run of quite a few engine moves in a row (especially since they aren't independent, some positions are easier to play than others).
Second, as Magnus has said in the past, if he has the ability to consult an engine at a single point in the game (of his choosing) he would be unstoppable. The reason is that in each game there are relatively few 'critical points' at which the result is decided.
That'd be really funny. Chess then became all about making a good move, but not too good, lest it may accidentially match with a chess engine and get you disqualified.
The meta would then to put the opponent in a spot with only one viable move option: They either get disqualified on the spot, or slowly suffer because they now lost an important piece.
I was never really good at chess, but even when playing async games with friends over gameknot(?) I'd often used the "if opponent does X, do Y" feature because some moves were just obvious.
Also, from what I gathered, you can instruct most chess engines to supply you with a list of moves for the current board state. So instead of picking the best move all the time, pick another good enough move to avoid your suggestion.