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.
Human players are dealing with both human limitations and human limitations which really changes the game. So a grandmaster can for example benefit from playing a slightly weaker but less well known opening that they have recently studied in depth with the assumption that their opponent hasn’t done the same.