Bergeron's 65 years old. Until recent years, that was pretty much a "you're done" age in game shows. Barker, Sajak, and Trebek all stretched that out, but they were all on long-running shows at the time.
Also, Bergeron has experience with replacing the "definitive" host (on Hollywood Squares), and he did quite well. Would he really want to go through that again, with far more scrutiny?
I get the sense that Bergeron doesn't feel the need to get back in the game.