That's a good idea.
BUT, that would totally take out the Element of Trading. That means, your Pokémon can't get boosted experience points. And what? Beating EVERY Trainer without training? I suppose EV-Training would be out of the question then? Hmm, a Pokémon Game that doesn't include hours of long and hard EV-Training would be pretty bland, seeing as EVs, IVs, and DVs can help Pokémon out a lot.
And choosing which region you start in... That might give you an unfair advantage. In Gold, Silver, and Crystal, you started from Johto but can travel to Kanto, yes. But Oak never gives you a Charmander, Bulbasaur or Squirtle. Your first starter is your only starter. With a game that includes all twelve starters, then it would be too easy trying to fill up your PokéDex.
In other words, that idea is good, but it just won't cut it, being a Pokémon Game and all...
Side-Note: Don't double post. If you double-posted by accident, PLEASE delete the other one by using the Edit Button found at the bottom right corner of your post.