I think all Pokemon should have an HM slot in which only HM moves can be put into. These cannot be used in battle and can only be seen in the move learning interface. Obviously they can be used outside of battle.
PokéOne tries to stay as true to the original as possible for an MMO. Your idea is not bad but something like that just doesn't exist and would change the mechanic of pokemon as well . Having a HM slave with you is not that burdensome. I'd rather see the devs working on new content than realizing something like that