Multi-regional Champs?

[HeatPoetic]

So, I thought of something earlier. We saw Lance as the Champion in the first-gen games and then Ash won the Alola league. My question is this: couldn't Ash go back and beat the Indigo League now, making him Champ of Kanto, Johto, AND Alola? If not, why do you think?

 

[WyndonCalling]

Well, it would be interesting from a procedural perspective - if one person had multiple Champion titles under their belt, what does it mean to defeat them in a match? Would you have to challenge such a person as just the Kanto Champion or Alolan Champion, or would you take all of the titles from them in one go if you win? If it's the latter, you'd quickly get to a point where one person is all the Champions all the time, and each League is just another pathway to that person.

Sword and Shield slightly implies that you have to stick to a particular League and you can't have multiple hats across the world. Raihan is said to be good enough to easily become a Champion in another region, but it seems that he might have to drop his Gym Leader role on Galar in order to be able to do this.