IANAL, but my understanding is that that effectively is what SCOTUS does most of the time, i.e. very few issues make it to SCOTUS that aren't constitutional questions. In any case, there is not any higher court like you're describing.

The US Supreme Court is the original constitutional court. It invented the idea that courts can rule on the constitutionality of laws and governmental actions (in Marbury v. Madison, 1803).

Some more recent constitutions have established a separate court that only rules on constitutional issues, but the US doesn't have that.

you're talking about the US Supreme Court but it has been politicized over the years and leans to one party or the other instead of strictly interpreting the constitution. For example, many people believe it leans heavily to the right side these days.