It’s certainly possible that Kang himself discovered who was actually behind the TVA while in the form of Mr. Gryphon, and ended up getting caught and pruned into The Void as a safety precaution, where he then made it his mission to destroy everything that also got pruned.
Which is really as plausible as anything else at this point, such as Sylvie and Loki potentially teaming up with Kang to get everyone out of The Void, no matter how evil.
As well, I suppose the TV show would be purporting that Kang and Alioth are on the same side in this universe if that happened.
Though I guess that wouldn’t automatically explain why he couldn’t just time-travel himself out of there, considering Owen Wilson’s Mobius was able to use his TemPad to go back to the TVA.