What the law professors actually said is that “Section Three is self-executing, operating as an immediate disqualification from office, without the need for additional action by Congress.” At the state level, however, notice and an opportunity to be heard would be required before a secretary of state could disqualify Trump from the ballot and this determination, as you say, would be subject to judicial review. Any direct lawsuit in federal court (declaratory judgment that Trump is disqualified) would obviously also ultimately be reviewable by SCOTUS.
No way Section Three could trump Due Process which, of course, is mandated by the Fifth Amendment and in Section 1 of the 14th Amendment. Precisely what process is due, however, is another question.
But you are making a big leap in assuming SCOTUS would not “approve” a Trump disqualification if the state provided the requisite process and proof. That would depend entirely on what the standard is for an insurrection and rebellion, or aid and comfort to enemies. The theory is valid- it is right there in the text. Tribe and the law professors are certainly wrong in arguing the words should be construed broadly – just the opposite is true. But, where that line is to be drawn, no one knows. I’d guess it will be drawn closer to the Civil War than to Trump’s January 6 Clown Show.
That no prosecutor has charged “insurrection” is beside the point. Section 3 is civil -not criminal - with a much lower burden of proof than the criminal statutes prohibiting “insurrections.”
My concern, however, is that if a blue state disqualifies Trump, a red state will disqualify Biden and the election will be plunged into chaos until SCOTUS sets a standard and then each state will have to determine whether the candidates meet that standard.