Most presidents want to be followed by someone from their own party, though Trump may be enough of a narcissist not to care.

Much less seriously, Trump can't run in 2024 either. See, since he won the election in 2020, he's already had his second term...

I don't see why he'd let such a technicality stand in his way, when actually losing the vote last time around was not enough to persuade him that he couldn't be president anymore.