Only one Pokémon game champion never took that title in the anime
While every regional champion from the Pokémon games appears in the anime, not every single one appears as a champion.

There are a lot of champions in the Pokémon games, and the anime handles them differently. Still, all of them have been consistently portrayed as champions - except for one, that is, he's been around since the beginning.
Ash's opponent, Gary Oak, is based on the blue character from the original Red and Blue game, who is also the player's opponent in Pokémon and the grandson of Professor Oak. Due to the popularity of the anime, Gary was even suggested as a possible name for Blue in the US release of the game. The name Gary comes from his Japanese name Shigeru, as it fits the anime's mouth better than Blue. During the match, Blue beat the Elite Four ahead of the players, making him the defending champion who must fight as the final challenge. Blue went on to become a Gold and Silver Evergreen Gym Leader and continues to appear in-game, most recently as a talented trainer in Ultra Sun and Ultra Moon.
Gary, on the other hand, took a very different path than his game counterpart. gary is always on display As a very competent trainer, despite being rude to Ash. He somehow managed to get 10 badges in Kanto and made it to the Indigo League Conference, where he finished in the top 32, just behind Ash, who finished in the top 16. Instead of going on to become a Pokémon Gym Master, Gary explores Johto and enters the region's session, where he'll be in the top 16 compared to Ash's top 8. From then on, Gary decided to follow in his grandfather's footsteps and become a Pokémon researcher. Gary continued to appear in almost every iteration of the anime, and while he still had rivalry with Ash and later Wu, he accomplished a lot as a young researcher, joined the Dream Project with Wu and captured many legends Pokémon.
Gary's Divergence from Blue is a Good Thing

Gary has evolved into a different character than Blue, mainly because he has been a major character in the anime. Most champions are introduced after attaining this rank, the only exceptions being Iris and Gary. Alice wasn't the game's Pokémon champion when she was introduced, and just became a later result. While it was known from the beginning of the anime what Blue's character arc was going to be, the decision to go differently was clearly deliberate. Despite his Pokémon proficiency, fighting isn't Gary's strong suit, at least not at a high level like Meeting. As Gary continues to outshine his rivals, it's clear they need to find a direction for his character rather than winning titles off-screen. Having him follow in his grandfather's footsteps even sends him back in Pokémon Journey as Wu's rival in his research-related quests.
Gary may not be a champion like Blue, but he is arguably a better character. At least, both versions of Oak's grandson can say that through hard work and persistence, they've reached the pinnacle of the Pokémon realm - just like Ash.