The above is from Article 3, Section 2 of the Constitution. Chief Justice Roberts wrote a paper on it and says it's pretty clear that Congress can pass a non-reviewable law.
In fact, they did so just about a year or so ago.
It's not clear at all. There's lengthy scholarship on this issue, dating back close to 200 years.
My position, as I've argued repeatedly on this forum, is that Congress cannot pass a law that is immune from Article III review. The reason why your argument fails is because you're reading that section of Art. III in isolation.
The first sentence of Art. III is mandatory. "The judicial power shall be vested...." The first sentence of section 2 is also mandatory: "The judicial power shall extend to all cases . . . arising under this Constitution . . . ."
Thus, reading Article III together, as we must, it's clear that Congress can limit the Supreme Court's appellate review. It's also clear that Congress can abolish lower federal courts, so some people have argued that Congress can create an "unreviewable" law, but this ignores the mandatory commands of Article III which clearly state that the judicial power must be vested in at least one Article III court, the judges of which must have lifetime tenure and salary protection, per section 1.
That is interesting. I hadnt been familiar with that. It begs a question, though. I think of FDR and how the Supreme Court kept striking down his socialist programs so he proposed to restructure the court with new members, giving himself a reliable majority. The outrage was too much for him to bear and he had to withdraw his idea to pack the court.
So if it was legal, why not just have congress pass the programs and make them not subject to review? Interesting.