Would the Supreme Court be able to strike such a law down if they themselves challenged it? They obviously couldn’t be impartial regarding a case like this, so who would rule on something like this?
You mean a referendum? The United States disallow it because “the country is a republic”.
You can even change the constitution by a referendum (never happend before, but you could).
Part of the original reasoning of the supreme court being appointed and not elected was for it to be above politics and allow for skilled specialists to be appointed, and honestly I’m inclined to agree with that thinking.
I do believe term limits are a very good idea for all offices though. Say, 12 years for elected positions (2-3 terms) and 8-10 for appointed to allow for individuals to really get good at what they do, but keep it short enough to get new blood in there and provide clear avenues for retirement, or moving into new offices as desired by the individual.
No, they would not.
In all Cases affecting Ambassadors, other public Ministers and Consuls, and those in which a State shall be Party, the supreme Court shall have original Jurisdiction. In all the other Cases before mentioned, the supreme Court shall have appellate Jurisdiction, both as to Law and Fact, with such Exceptions, and under such Regulations as the Congress shall make.