Maybe he could win a league, but would he be a better trainer? Not necessarily. By constantly rotating his team and training a new set of Pokemon every region Ash is giving himself a broader range of experience by working with a large variety of Pokemon, experience that he would never gain working only with the same six. There's more to being a good trainer than just having powerful Pokemon, and it is arguable that the experience gained by working with a multitude of Pokemon is more important than having six powerful Pokemon.
So to answer Bguy's questions, what switching out Ash for a new child would change for me is it would lend more dignity to the series. A show that ultimately exists to sell things isn't exactly wholesome to begin with, but it's totally possible to advertise for new regions and new Pokemon without having to make an old character throw out his old friends in favor of then; if only they chose to promote the latest generation with a new character who started with them. That they don't is what tilts the balance from a petty extended commercial to a petty and reprehensible extended commercial. Children deserve role models; a guy who will just dump his friends and has a broken work ethic is no good role model.
In what way does Ash abandon his friends? When it comes to his human friends, they leave him because their paths are separate from Ash's, not because Ash is dumping them. And his Pokemon friends are far from abandoned. Ash uses them from time to time in leagues and other important battles, and checks in on them while they're at Oak's lab.