Here's an interesting in the New York Times on something similar:
http://www.nytimes.com/2008/05/25/us/25exception.html?pagewanted=all
According to the article, 87 percent of all state court judges are elected. Also according to the article, the United States is the only major nation to do this: ie we already elect judges. So, if we're as free as you say we are, then perhaps the fact that we elect, rather than appoint, judges is partly the reason?
The point is, what I'm advocating isn't anything unprecedented or unproven. It would simply be an expansion of something we're already doing at a lower level and bringing it to the Supreme Court.
And, once again, if we can elect the other branches of government, there is no reason the judiciary should be seen in a different light. All three are supposed to check and balance each other, right?
I agree that a direct democracy is a bad idea (although I do think we should have more referendums like in Europe).... but nobody is saying that's what we should shoot for. What I'm after is equal representative government covering all three branches. A Supreme Court judge would be no more beholden to his constituency than a senator.