Actually, the Constitution says Congress by law is to designate which "officer", meaning "official", is to become President if the presidency and the vice presidency are vacant. It used to be the President Pro Tem of the Senate and now it is the Speaker of the House. No need or reason for the SCOTUS to get involved.
I agree. However, it also states that the House Speaker, if chosen, would have to resign the position. When the position is resigned that individual is no longer eligble to become President. It is a glitch in the system but you can bet it would go to SCOTUS to resolve.