Ash Ketchum's Age - Ho-Oh did it.

I'm not so sure about that.

So long as he keeps losing the Pokemon League challenge, he always has something to aspire to. For him, the happiness comes from the journey and the friends he makes along the way. If he ever wins the League challenge, this his journey is (metaphorically) over.

Sure, he can continue on to new locations, and find new Pokemon. But he will feel like he reached his peak. He wants to be the very best, and the Pokemon League Champion is the very best in his mind. He would achieve his goals, and have nothing to strive towards.

That's why he must not win the League. Also, because it would break the Pokemon anime formula.

The chase is better than the catch, my friend