Ok, here's what I have to say/ask:
While being a 'Pokemon Master' is quite subjective, I define it as simply being the best trainer in the world ('I wanna be the very best like no one ever was'). So going by this definition, Ash winning a league would not make him a 'Pokemon Master'.
Ash in my opinion, needs to win a league (obviously not counting the Orange League) because if he doesn't, then it wouldn't be good for young kids as it may make them believe that some things in life are just too hard to achieve no matter how hard you try so for kids aspiring to be sports stars, models, actors/actresses, doctors, lawyers, etc. it wouldn't be good for them.
Ash should also win a league simply because he is a good guy and deserves to win one and he is the main character and the main character/good guys usually win. And if he does win one and goes to a new region and loses to some random trainer/gym leader, then maybe some people will think that's stupid but you can relate that to sport in real life where a team might win a competition one year but be terrible the next year.
As for an appropriate ending, I believe perhaps a Dragon Ball Z type ending would be the best. Ash wins a league and battles an Elite Four member and wins, and then goes off on a completely new journey, perhaps helping out some developing trainers?
And finally, I want to ask, just out of interest, does anyone know of any statistics regarding the popularity of the pokemon anime? Because I know the games and the overall franchise is still going strong but I thought perhaps the anime might be experiencing a slide with Ash not winning any leagues and all.