I hear you, but this still focuses only on the effect of an ineligible president having served. And on the House’s role in counting votes, etc.
In effect, you seem to be saying if the House gets it wrong — if in fact, it allows an ineligible person to be seated as president — there is no remedy. Again, I’m not focusing on the effect of the ineligiblity on that president’s acts (treaties, etc.) But surely there must be some way to remove an ineligible person from office based solely on his ineligibility. Or are you arguing that, by virtue of being seated as president, there could never be a challenge that the president is ineligible?
Also I have yet to see what process the parties take in nominating, and the House takes in seating, to ensure a person is eligible. If no one can even produce a Supreme Court precedent on what, exactly, constitutes “natural born citizenship” (as opposed to citizenship), how in the world do the parties or Congress even know what to look for?
As I said, I haven’t followed the legal briefs, but it seems to me that if there are questions that are legally cognizable, they need to be sorted out now and evaluated before the next presidential election.
My read is that impeachment would be the solution. This may be why impeachment can be widely defined.
As to the background check on eligibility, the process is up to the House. Perhaps after this they should pass some rules.