Insufficiently checked and balanced?

I have a question for you legal/constitutional experts out there: Why are supreme court justices appointed and not elected? What did the framers have in mind when they made these appointed positions? It seems logical to me that if the judicial branch is to be able to check and balance the other branches of government, then they should be elected independently by the people of the United States. I realize this wouldn't be a practical measure for all federal judge positions, but one might at least consider it for the supreme court. As it stands now, it seems that the executive and legislative branches have too much say in the makeup of the court. One could argue, however, that requiring the other two branches of government to agree on a judge creates a balanced enough approach. On the other hand, what would the ramifications be if justices were subject to general election? I would love to hear your comments.