Not wasting time with claims would be another very practical advantage.
A further variant for fairness purposes: let each player bring their preferred chess engine, instead of arguing about the choice of only one; and have each player run both engines for mutual anti-cheating verification.
Then either the two engines agree on the best move (likely case if they are both strong) or all moves that either engine considers better than the other engine's best move (at least 2, usually not too many) can be interdicted.
A further variant for fairness purposes: let each player bring their preferred chess engine, instead of arguing about the choice of only one; and have each player run both engines for mutual anti-cheating verification. Then either the two engines agree on the best move (likely case if they are both strong) or all moves that either engine considers better than the other engine's best move (at least 2, usually not too many) can be interdicted.