I think this is a nice idea, and would even out gameplay a lot. I was always torn about my starter in the canon games, and in Citrite I tried to ensure your starter wasn't specially unique for that reason.
I'd enjoy getting rid of having unique starters that no hardly anyone else has, because it'd make my Pokémon feel more interchangeable and less bound down. It'd also be more like if we started our journeys as, you know, regular trainers? :P