There are rules for the game that are perceived as fair.

If one participant goes changing the rules in the middle of the game this 1) makes rule changing acceptable in the game, 2) forces other players to analyze the current (and future changes) to the game to ensure they are fair.

Cutting the deck probably doesn't affect the probability distribution (unless you shuffled the deck in a "funny" way). Allowing it makes a case for allowing the next changes in the rules too. Thus you can end up analyzing a new game rather than having fun playing poker.