It got progressively worse after the first two seasons, which were decent. For those, you could pretend that it was just dumb luck. But after that, it got pretty ridiculous. He seems incapable of failing, which is obviously a pretty generic Stu trait.
On the other hand, this is technically a children's show, and kids are not going to be interested in a protagonist who loses all the time. I have a personal belief that this is also the reason why they continue to change his companions after every few seasons.
It's odd, because every few seasons (usually when his companions change) his character development goes back to the very beginning of the series and then starts over, but he continues to win matches due to his high-level Pokémon.
As a side note, the first three or four victories he won were just pity victories, which is not as implausible as a beginning trainer.
So in the end, yes, he is borderline Stu, but not totally Stu. At least, not yet.

Season one was okay, season two, eh, worked too. But it just went downhill. And I'm sure there's other ways to keep kids interested. Like having him, finally, win a damn league and getting him out of the show. Like the games did.

It's typical in a kid's show for the protagonist to be able to solve a wide variety of problems, but Ash is pathologically incapable of failing, even when a problem falls completely outside the range of what he could conceivably do. If he encounters a problem that determination, friendship, and deus ex machina can't get him through, the writers try to cover up that there was ever a problem. This is particularly bad since he, due to writing laziness and Aura of Smooth, is able to cure the psychological problems of every single Pokémon he meets without any effort whatsoever, especially fire-types.

The Unova series is really awful about this. One episode is basically "Oh, hey Tepig! You've been abandoned by your Trainer, just like every other fire starter I've ever met, but with the added condition that you've been alone, forced into a life of desperation, and expecting your Trainer to return for what may have been months? Here, come with me, and everything will be all better. You'll literally forget that you ever had any sort of problem three episodes from now!" You know, despite the fact that Charmander/Charizard's character was interesting due to the way it reacted to a very similar problem even seasons after Ash found it, and Charmander wasn't even suffering visible abandonment issues when it had been found. The Tepig was emotionally scarred by its original trainer tying it up and practically starving it to keep it from following him, and Ash just takes Tepig in and it drops any repercussions that it might have due to an objectively horrible past.

That's Ash's main Canon Stu trait for me, aside from the one mentioned before where he wins battles with no effort and horrible strategies. Whenever he's directly involved, logical responses to anything, even responses that could make interesting subplots or provide distinguishing experiences for characters, go out the window.

That, and the fact that he was "the chosen one" for two separate prophecies and one secret organization in three completely unlinked regions, but that's peanuts to the bad psychology and the total affronts to logic he creates.

... is that Ash, for NO REASON WHATSOEVER, goes back to "incompetent kid" as soon as he steps into a new region.

For examples, towards the end of Sinnoh, Ash manages to use his fairly regular pokemons to great effect against rare ones thanks to his unconventional strategies. He's the only one to actually manage to knock out Tobias' Darkray This guy has six Pokemons, like Ash and al the others. We only see two, as everyone who isn't Ash gets curbstomped by Darkray alone and Ash barely manages to defeat it with all of his six pokemons, only to be finished off by Tobias' second one, another rare uber-powerful one. Yeah, sure. (Seriously, I kinda want to put a Gary-Stu-wanted-dead-not-alive warrant on that guy.)

Clearly there's something wrong in all of this.

Then Unima starts, and Ash is so incompetent and obnoxious that I facepalmed after watching the first couple of episodes. Where the hell went all of his character development?
Not to mention that poor Pikachu got himself nerfed again. Although I kinda understand that - by the end of the first arc that cute yellow mouse was able to go against a Dragonite and lose by a very little margin. (If I recall correctly, Dragonite fainted just a couple seconds after Pikachu)

Eeeyeh... I didn't mean a generalization for all kids' shows, I meant because it's targeted at a demographic consisting of mostly kids that like to idealize people. So what better way than to idealize said protagonist? Of course, there are better ways than doing so, instead of Stu-ifying him but yeah, creators are creators, can't say much about that. Plus the original seasons had 'The Power of Friendship' theme for the most part, so I guess Status Quo is God in this case.

I think it is justified. I remembered an episode in the first season of Pokemon, where Ash had to release Butterfree since it is fully evolved and has to mate. I assume Ash subconsciously banned his Pokemon from doing the same. But Charizard may throw my hypothesis to the dumpster.