To be a “political question” in terms of the judiciary, the Constitution has to directly and specifically give the job to a different branch of the government. Where does the Constitution ever give any other branch the job of determining who is or isn’t eligible to be President? Specific reference, please.
If a political process (other than the political process of amending the Constitution) nullifies the Constitution then we are not a Constitutional republic.
I think your observation is really more generic. When ANY of the bodies refuses to abide by its duty, or to respect the limits of its power, then the constitution suffers. Any of the three bodies is capable of nullifying the constitutions, and I dare say, all three HAVE; and in some case, via cooperation.
Say, for example, SCOTUS rules that anchor babies are natural born citizens; even if raised an foreign citizens in the home country of their parents.
Or, for another example, Congress fails to even inquire as to whether or not a dual citizen is qualified.
Anyway, my personal point of view is that all the branches are derelict, and we are NOT in fact, under the constitution in a number of legal areas - presidential qualifications being one of many areas that are corrupt beyond repair. "Coin Money and regulate the value thereof" is probably the biggest, but so too are commerce clause, 2nd amendment, and takings.