I think that it would be really neato to give starter mons one egg move, like in PMD games… Would be a useful mechanic for new players, for whom it will be a while before they can get their hands on a heart scale (without relying on other players) and egg moves from Togetic.
For some mons, the egg moves can provide type coverage (esp grass types), or can even be one of the broken healing moves, Refresh or Aromatherapy. For others, like Togepi or Ralts, who start off without offensive moves, egg moves are essential in order to make early game more viable.
I can provide a list of one egg move per starter.