I honestly don't see the necessity for a dragon starter. It's just unnecessary and too overpowered. Unless you're suggesting every trainer and their mothers carry ice beam and dragon pulse everywhere they go. I personally think that they won't go down that route, it just gives the specific starter too much advantage over another.
As for the movepool thing, having to learn a particular move just to counter the starter you are weak against is just... bad and annoying. That means your mon will lack diversity. So every run you'll have to carry Ice Beam or Dragon Pulse. But wait! What if Ice Beam was found like at 7th gym? Boom!