Do you know so little of the Constitution?
Congress can impeach judges - even Supreme Court Justices. That they have not chosen to do so is not an indication that there is not a check and a balance on SCOTUS legal interpretation.
If your beef with an elected Republican form of government is that there are unelected judges - do you think ELECTED judges would decide the law more justly - or would they base their decisions on what was popular?
Do you think judges deciding the law based upon popular opinion would be a good thing?
Think about the status quo that has resulted from the fact that activist judges are not accountable to the people. An elected politician that deceived his electorate and participated in the appointment of an activist judge—would such have the propensity to impeach the very justice he got into the SCOTUS? Now if I'm not mistaken, even the USSR's Supreme Soviet had such powers over the Politburo as the Congress has over the SCOTUS; but communism encourages lack of morality. All down to accountability, which a republic is supposed to preserve.
AIR, the notion of appointed Supreme Court justices was as a shield in the case of their making unpopular decisions—but all of the unpopular decisions that have been taken in that branch of government have been in favor of the left, not in favor of preserving the rule of law as delineated within the Constitution. Nowadays, we have
justices such as this one who openly trashes the very Constitution that she swore by oath to protect—and she was not elected.
This is not a problem I have with the republican form of government; this is a problem I have with the abuse of power within its framework, and the violation of the oaths taken to protect and preserve the rule of law as the Constitution is supposed to keep intact.