They should just make HMs more worthwile imo. Most of them are weak, too many of the same type forcing you to stack them on one pokémon (I'm looking at you, water-types!) or outright pointless. Cut serves no purpose in battles once you get Strength.
And Game Freak should be capable of limiting trades of pokemon that know HM moves. It's an inconvenience, sure, but not as inconvenient as having to get a Heart Scale to relearn a move because you couldn't delete an HM.
If anything needs to be improved in these games, it's the HM moves.