What are the advantages and disadvantages of having a branch of government that is not democratically elected? Political science homework help

The lecture this week suggests that the U.S. Supreme Court is the least democratic branch of government, and yet it serves an important function in our democracy.

What are the advantages and disadvantages of having a branch of government that is not democratically elected? Would you change the way the court is appointed?

—It just have to be 100 words for the minimum—