There is nothing that cannot be framed in terms of a question of law or fact. Of course, a court would be mentally capable of finding facts. That is not the problem. The problem is that the Constitution has delegated that responsibility to another Constitutional actor - the Electors.
There is a similar example of which everyone is familiar. Suppose a person is tried for committing a crime. The defendant takes the witness stand and confesses his guilt. But, at the end of the case, the jury comes back with an acquittal and then tells the court that even though each member of the jury is certain that the defendant is guilty of the crime, the jury has decided to acquit the defendant because the jury does not want to follow the instructions of the court or the law. Under those circumstances, there is no reason that the Supreme Court would be mentally incapable of making a determination that the defendant was wrongfully acquitted and that he in fact committed the acts constituting the crime. Nevertheless, the Supreme Court would be without power to convict the defendant because the Constitution commits that decision to a different Constitutional actor - a petit jury.
For the same reasons, I believe that a court has no right to participate in evaluating the qualifications of candidates or choosing presidents. Electors choose presidents. And, since you as a voter participate in choosing Electors, I believe that you have a duty to evaluate the qualifications of candidates and that you should not assume that a court can perform that function for you.
We have been electing presidents for more than 200 years. You will not find that our Supreme Court has ever disqualified a candidate for president or that it has ever even claimed to possess the power to disqualify a candidate for president.
Courts have removed ineligible persons from ballots and from office.
The particular eligibility requirements for the Executive differ from those of other offices, but there is nothing that sets that office apart from others as regards determination of eligibility by the Judiciary when a case is brought.