What "Pokemon Master" actually entails is never really elaborated on, but even if he does become Champion, that doesn't necessarily mean he'll become a Pokemon Master. According to Ash, "Pokemon Master" is beyond "Champion", so even if he becomes regional Champion, that still won't make him a Master.
But honestly, the idea of him becoming Champion before the show's end is ludicrous. Just the idea of him defeating a member of the Elite Four would already be a bad idea. The Elite Four are the best trainers a region has to offer, and the Champion is even better, the very best of the very best. If Ash were to defeat even one member of the Elite Four, then he'd be amongst the top twenty or so trainers in the entire world. This would be terrible for story-writing purposes, since that would mean that only other Elite-ranked trainers would possibly be able to challenge him.
Half the show is centred around Ash's journey, and tournaments are simply the climax of that journey, the goal that he set out for. By making him Champion, the "journey" aspect of the series would be completely torn down, and the show would be nothing but an unending battle-fest. Pokemon isn't that kind of show.
Now there's the argument that he could do what he normally does and and start fresh in a new region with just Pikachu. But that would be even more senseless than what he's doing now. Becoming Champion isn't simply a matter of having the strongest Pokemon, but also being a sharp strategist and unrivaled tactician. If Ash wants to become Champion, he'd have to have skills far beyond what he currently has, and by actually becoming Champion, it would be confirmation that his ability as a trainer is of the highest class. This would make the concept of him losing to anyone other than an Elite Four member or Champion absolutely ridiculous. Even if he started over, his sheer skill would allow him to plow through any league. And if he actually LOST to another normal trainer or gym leader, then everyone would simply cry foul at that.
Note that Ash is a normal trainer. In the beginning, he didn't have any particular talent for Pokemon Training, and the skills and ability he displays now are the result of journey after journey. In other words, he got this far not through innate talent, but sheer hard work and determination. And he's up against hundreds, thousands of other trainers who also work hard to get where they are, some simply born more talented than he is. Furthermore, the Elite Fours and Champions of the various regions are trainers who have managed to get to the very top AND defend their positions presumably for several years, at least. In other words, these trainers have gone undefeated for SEVERAL YEARS, despite hundreds of ambitious trainers just like Ash challenging them constantly. Only the very best of those Trainers will be able to win a tournament, securing the right to challenge them, and even then, only the very best of THOSE trainers will even be able to take on the first Elite Four member and possibly win.
The main problem here is that people are constantly comparing the show to the games. In the games, a random ten year old in a no-name town journeys to become the most powerful Trainer in a given region. But, see, for the purposes of gameplay, the protagonist of each of those games is constantly viewed as an immensely talented trainer who was simply born with innate talents that allow them to obliterate any trainer in their path and become league champion in very little time. The protagonist defeats trainers many times more experienced than they are and obtain the title that hundreds, thousands have sought for all in a matter of maybe a month or so, tops. But that wouldn't work in the anime. If Ash won every single battle, that would be boring. If Ash became the strongest trainer, that would also be boring.
Ash is still young. He's ten years old. While it's true that the anime's concept of time is a bit... okay, COMPLETELY nonsensical, the fact remains that he's been on his journey for less than a year. The fact that he's managed to get to the top four of a Pokemon League tournament is nothing short of ASTOUNDING, and he got that far through sheer hard work and unrelenting determination. He's still learning, still growing, still developing his skills, and someday, surely, he'll be able to see the realization of his dreams. But not yet. Not now.
Of course, there's the argument that they should simply replace Ash for another trainer. But do we really want that? Do we honestly want another hundred episodes of a complete newbie kid making amateur mistakes, slowly and steadily growing to become a better trainer? That's just opening up a whole 'nother can of worms. Many viewers were barely able to stomach Ash's perceived "stupidity" during his Kanto journey, and a repeat of that won't please anyone. That's not even going into the sheer amount of outrage that will no doubt erupt at the thought of Ash, the same character so many fans have grown to adore over the years, being replaced by what will inevitably be viewed as a replacement scrappy.