I think that's a weak excuse. So just because during Gym Battles they have to change how they do their usual battling strategies that's why they're seemingly concluding Ash's story and doing an anthology series? I can think of several ways they could handle the Dynamax battles in the anime and if the writers wanted to they can do so too.
If you want one of my thoughts, explain that when a Pokemon Dynamaxes the size increase makes moving around very difficult so the Pokemon just have to duke it out when they're big. The Pokemon only remains Dynamaxed for three moves when they return to normal, so battles would either be the Dynamax Pokemon sharing blows or a normal Pokemon working around the Dynamaxed Pokemon's weakness (being bit and slow) and either defeating it when its big or getting it to use up its three moves so the battle can return to normal.
In this way, you can make it so Ash has a few Pokemon he goes to Dynamax while others he prefers not to because they're better battling small then big. Infact, with Pikachu refusal to go back into its Pokeball, they could make it so Pikachu never Dynamaxes but rather battles small, darting around its Dynamaxed opponent if it ever goes up against one.
Now they would have to explain why Ash wouldn't be using Z-Moves anymore, but that's an easy excuse of the energy needed to use Z-Moves are Alolan exclusive so Ash's Z-Ring no longer works outside of Alola.
As
Vengeance417 said, Ash does have Pikachu's Pokeball because that's how Pikachu is recognized as Ash's. From the trivia section of Bulbapedia's page on Ash's Pikachu:
In the first season it made three appearance (first episode where Ash gets Pikachu, in the Brock Gym Battle where Ash tries recalling Pikachu because it was trapped by Onix's Bind, & when they were trapped in a cave on a snow top mountain Ash told Pikachu to get in its Pokeball where it'll be warmer).
It was absent for Johto but made a quick appearance in Hoenn where Ash was cleaning all of his Pokemon's Pokeballs.
It was then absent again for Sinnoh and Unova until XY where it surprisingly made two appearances (in the Battle Chateau where custom dictates before a battle starts you and your opponent tap your battling Pokemon's Pokeball & and in the Pokeball Factory where Team Rocket got a hold of it and Meowth began chasing Pikachu around trying to recall it).
Finally up till now has been absent through Alola though it of course made an appearance in the movie retelling of the first episode.
Though should be noted after its debut it no longer has the thunderbolt symbol on it for whatever reason.
As I said, on paper the Alola League is the perfect League for Ash to win. But the execution of the entire season didn't really build up to it. Infact I would be surprised if the decision to have Ash win was a "last minute" thing. As in the writers weren't really thinking about it until Sword & Shield was announced and they saw all the things it was bringing both new and back (notably a typical League structure after they spent an entire gen doing whatever they felt they wanted).
All I'm saying this victory was done not because it was an acceptable conclusion to Ash's journey but because the writers don't want to go back to a typical Pokemon journey structure.
