[Dr. Franklin]

That’s not a constitutional remedy, so it won’t work.

The constitution doesn't provide for a lot things, like popular election of the president. The constitution puts few limits on the power of Congress to pass a law like the quo warranto statute, and fewer on the judiciary to interpret it. In a common law system such as ours, the constitution is pretty much what the courts say it is, unless people want to take up arms to decide an issue. (Succession was such a case.) If push comes to shove, an army of phantom voters can't fight.

[Boogieman]

“The constitution doesn’t provide for a lot things, like popular election of the president”

I think you mean popular election of Senators, since we don’t have popular election of the President. But the Constitution of course does provide for the popular election of Senators, in the 17th Amendment to the Constitution.

“The constitution puts few limits on the power of Congress to pass a law like the quo warranto statute”

Perhaps for ordinary federal officials, but that simply isn’t true when it comes to the President. The Constitution specifies that there are only 2 methods to remove a sitting president, which means that any additional methods must be added through the amendment process, just as the 25th amendment process was added. If what you were asserting were actually true, then Congress could have just passed a regular law to enable removal of an impaired President, but they could not do that, because it would be unconstitutional, just as your “quo warranto” fantasy is.