The subject I am curious about is this.
Should Ash get a new badge if he ever wants to get into Kanto league again. Or will the badges collected to enter the Kanto league always have validity?
Once Pwc is over, he can try Ash Kanto league again if he doesn't need to collect badges again.
Knowing him, Ash would probably challenge them again specially since there's been changes.
He can get legit matches against Misty, Erika, and Sabrina.
He can face the newer gym leaders Forrest, Janine, and whoever runs the Viridian Gym now.
He can get rematches against Lt. Surge and Blaine.
As for the actual rules, I'm sure each badge has some kind of serial number equivalent that makes them usable once. If it's anything similar to Contest Ribbons, they can last for years as long as you haven't registered them for the grand competition as seen with Johana's old rival in DP. So that means Ash would have to collect them again. Although... I can't see this situation really happen. The only exception is if they make a new game that takes place in Kanto that doesn't follow the old formula and could potentially use different gyms and have newer towns and cities.
For example, Ghost and Dragon would make more sense now to be Gym types instead of Elite Four as there is only one Kanto line for those Pokémon. It would be interesting if they have a Ghost-type Gym in Lavender Town for example or even a Steel type gym that uses the Magnemite line and imported the Alolan Sandshrew line as well. They could actually do a Dark-type gym in Kanto now by importing the Alolan Ratatta, Meowth and Muk lines.
But I got carried away. Short Answer: I think he would have to challenge them again if he wanted another chance in the Indigo League. But I don't think he would do that in the current state of Kanto in the games.