Obviously the intent of the founding fathers and the people is that insurrectionists cannot be permitted on a ballot, not by any officer of any court or state.
It’s the same as the Fourth Amendment. If the prohibition on warrantless search and seizure has any meaning at all, it is a command to every law officer, attorney, and judge, as to how they must do their part of their job in the matter, and that rule is that: if the constable blunders, the criminal must go free. The remedy is implied by the text, because if it’s not the text doesn’t mean shit.