> If he's impeached and convicted he's prohibited from holding office again.

Technically, that's not necessarily true: if he is convicted the punishment can consist of any combination of removal and bar from holding future office. In theory, he could be removed but not barred on conviction, though that seems improbable and, AFAIK, every actual conviction in an impeachment trial (most such trials have been of federal judges) has resulted in both removal and bar.