A problem I see with it is, well, if Rivalry Orb shards are only obtained by getting them from Gym Leaders, and can only be used on a single Zangoose or Seviper, wouldn't that make completing the Dex impossible?
And the main problem I have with having Leaders give out non-TMs is that the TM moves are treated kind of like the Leader's signature move. You can't exactly do that with part of a Rivalry Orb or some other equippable item.
It's a solid idea, but I think it would be better if we looked for TMs that worked first, and kept this as a backup idea.