From the inception of Earth C, there has to already be ancient temples and the like for the next set of players. Do you think those players will have anything to do with the Alphas or Betas?
Another thing: What if the Alphas and Betas played Earth C's Sburb together? Would they even be allowed to do that? Would their godtier-ness be stripped from them?
I don't know that there are any frog temples on Earth C beyond what already existed, bc it's the same Earth as the Earth in the Alpha timeline, which had sburb technology so the alpha kids could play, which they did. I think the advantage of taking the same planet and putting it in the new universe is specifically so it isn't targetting for destruction. Tho, we do know its ultimate fate. Eventually, the planet will die, and become home to Calliope and Caliborn on the meteor.
The lack of any functional sburb technology on Earth C is also why Dirk and Rose had to leave the planet to search for one in their universe that did have sburb technology, which we know took at least 3 years of searching, so it seems that planets seeded with sburban technology aren't all that common.

Have you read Beyond Canon? Knowing some of the characters might potentially give us candidates for who could enter another Sburb session, although everything remains to be seen...
A previous player entering a new session is a really fun idea. My guess is that with how intertwined Sburb is to the continuity of reality, it would be one of those things that Paradox Space would not allow to happen in the first place, or at least create a doomed timeline if it did. But, hey, crazier things have happened, and it would be absolutely in-line with Homestuck to add a whole layer of new bullshit and end up with someone who has godtier^2ed or something like that.
The technique is to use hot oil to elicit a response