You're completely missing the point of the supreme court. It's explicitly not a democratic institution; it's purpose is to protect the constitutional rights of the minority from the tyranny of the majority. The other two branches are democratic; isn't that enough for you?
Surely you see the point of the US being a republic; rule by law, not by men. In your vision of the supreme court, if the majority decided they wanted to lock up some minorty and send them to gas chambers, the court couldn't do anything to stop them because the populace would vote for it in a referendum. That kind of thing has happened countless times in history in countries that didn't have a strong court system capable of protecting people's rights from the tyrrany of the majority.