Short answer, there is no trainer.
That's the punchline to the whole Pokémon Master thing. It's not a real rank. It's not even a real eligible goal.
It's essentially a motivation drive. To be the very best, like no one ever was. It is beyond any Champion or Elite Four. Beyond catching em all.
It's a never-ending journey to be the best Pokémon Trainer... or really any career involving Pokémon. As long as there's something new in the world, be it locations, Pokémon, people, and challenges, etc. Ash will pursue it. Just like how Goku will pursue tougher opponents for his entire life despite being old enough to retire.
That's why Leon's greatest fear isn't him losing. It's actually reaching the top and have no more challenges left. He is the closest person to the definition of a Pokémon Master and it's not because of his skills, but rather mentality. Every trainer's worst fear in the franchise is having no challenges left. That's how you know you're the best.
Much thanks for providing much dialogue on your take on what a Pokemon Master is.
Unless the franchise or anime had retconned its concept of how a trainer obtains the rank of a Pokemon Master, its my understanding that the title of being a Pokemon Master, was a prestige rank, something equivalent to the mechanism of how a scholar obtains a high level academic degree (Masters or Ph.D), which could only be attained through vast accomplishments, such as winning league tournaments and championships.
Based on what dialogue I can recall from the series, a Pokemon Master was described to be a trainer whose gained much wisdom in the ways of understanding pokemon, and has phenomenal battling skills. However, the process of getting there is very challenging, which not many trainers are able to achieve.
Overall, I never took the title rank of Pokemon Master to be a visionary goal constructed by a trainers personal ambitions, but as a something that could be achieved , especially if the goal towards obtaining it is shown to be acknowledged by many world class trainers, and world renowned professors such as Professor Oak. The title wasn't something a 10 year old, such as Ash, made up, especially if was educated about the knowledge of how to get there.
For example, one could obtain the ultimate martial arts skill rank of becoming a blackbelt or master of a particular practice to be a sensei of a dojo, but the rank does not acknowledge them to the "THE BEST". That can only be decided in tournament battles.
