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I don't really buy the explanation that winning a league champion title would spell the end of his adventures. Like other anons have said, the title of a Pokemon master is something completely different, and is clearly more about the journey than the destination. A true Pokemon master is something more than just a winner of tournaments. If the writers of the show wanted to, they absolutely could make Ash dash off to whatever new region or challenge there is. Hell, changing the last generational shift so that Ash actually won the Kalos League and then went off to live in Alola for a while with Pikachu and his mom would require minimal changes to the events. I don't buy for a second that the writers are unaware of this.
But what is Ash as a character, really? In the video games, the protagonist is allowed to be a wunderkind who sets out on their journey and easily beats down all opponents, kicks ass and takes names. Ash, however, often struggles with battles, sometimes even against less experienced battlers. He isn't always the smartest kid around, but he does try. Ash is the everyman, the average guy trying his best. It might be a little cynical to have him 'lose' every time in a show aimed at a young audience, but Ash keeps his spirits up the majority of the time, and looking past never getting first place, he does generally place very well in all the regional tournaments. He often is the hero of the day, fighting villains and injustice. Who's to say he's not well on his way to becoming a Pokemon master?