Also Home can barely function as a storage & trade app as it is, the idea of bolting on a battle system to it is horrifying.The closest I could see would maybe be a battle system built into Pokemon Home, but they'd still have to include UI and functionality to pick a Game Format for things like "does Zacian have its new stats? Is Snow/Hail legal? What's the Pokedex?" and the like, at which point it's too much to sort through compared to the ML games doing that innately. Slowdown and game crashes at tournaments? Eh they're buying the game anyway.
And I can't imagine Nintendo would be keen to approve the Mobile version having a way to battle anyway. And no way they bother with the console version.