I don't like this change at all. HM is fine as far as damaging-Gish spells go. The problem is it is a damaging spell and attaching it to a bunch of class abilities really drives the class a specific direction, one which lacks thematics and flavor and further specifically encourages weapon use on a class that is a half-caster at its base.
If you are going to tie it to class like they have done, I would like it better if you just took away the damage completely and give you advantage on all skill checks against the marked target. Keep the mechanic of moving it as a bonus action. If you did this you could also take away concentration too since you would not be getting any damage out of it anyway.