Just elect the bastards every four years. It's not like they're not political as is. Might as well have some choice in the composition of the Court. Or of course, ideally, slap on term limits and give Congress the power to veto a Supreme Court decision.
Leaning neutral on the OP, but, that really is a terrible idea. The Supreme Court (and most inferior courts) are meant to be a check on the will of the majority. If we're going to democratize everything, we may as well do away with judicial review.
Amen, we need a check on the tyranny of the majority.
I don't really mind term limits, but electing judges is a bad idea all around.