There is a real problem here that needs addressing. That is, every year, the 13 appellate courts send some 30,000 cases up to the SCOTUS, that can hear maybe two or three dozen. This is terrible negligence.
But using simple math, creating a SCOTUS with 13 justices will not even make a small dent in this number. But what would is creating a “Second Court of the United States”, to act as a ‘screen’ for the SCOTUS.
Each justice of the Second Court would be under the guidance of a SCOTUS justice, much like they guide the appellate courts today.
“Mosquito cases” could be ‘swatted’ by the Second Court, or decided, or returned to the appellate courts. Particularly important cases, and cases that can be bound together, can be directly referred to the SCOTUS with the Second Court opinions attached. In the latter case, this would help the SCOTUS justices to form their opinions faster.
As an example, cases involving minors in public schools are the atherosclerosis of the federal court system. Similar cases every year with no definitive conclusion. SCOTUS justices should not be deciding teen girl skirt length every damned year.
No matter how many federal judges want to act like dumbasses and agree to hear such cases, “to show the youth the *importance* of the federal courts”, they should *never* appear before the SCOTUS. The Second Court would thus be a shield that the appellate courts failed to be.
I happen to be a lawyer, so I can give you a little insight why your analysis seems right, but is actually a little misguided. The Supreme Court does not exist to right wrongs. It’s real purpose is to settle disputes between the Circuit Courts below about what the law means, and to reverse seriously bad interpretations of the law by the lower courts (even if there is no dispute between the Circuits).
So if one Circuit interprets the law one way, and another interprets another way, the Supreme Court decides which is right. The fact that one of the parties in the litigation got a raw deal is not the Court’s concern for the most part. That is inevitably going to happen from time to time no matter how many levels of appeal you have, and you’ve got to draw the line somewhere when you decide how many bites at the apple you’re going to allow.
In our system, the District Courts are given primary responsibility for making sure the parties to the litigation get a fair hearing, and the Circuit Courts are given responsibility to review what the District Court did in that respect (because sometimes the District Court judges make mistakes). The Supreme Court merely focuses on making sure that the case law reflects a workable or correct interpretation of the law so that when the next case comes down, the judges below will know how to interpret the law.
The way to look at it is that the Court doesn’t do what it does for the benefit of the litigants, but rather for the benefit of the lower courts, which need some guidance in interpreting the law. A lot of the cases that get appealed to the Supreme Court do not present issues like that. They are what you are concerned about, i.e. that someone thinks he got a raw deal. The Court sorts through them and finds the cases where it can make a valuable contribution to clarifying the law, and throws out the rest. Sometimes that means someone gets a raw deal, but as I said, that happens.