No U.S. House Member has ever served without being elected. Even though U.S. Senators are more powerful than House Members and are no longer appointed by state legislators when serving a complete term, far too many states have have this odd anachronim of governor selections-- leaving us with two of our largest states (NY and IL) soon to have Senators only accountable to the governors in NY and IL who appointed them.
My colleague David Moon had a good oped in The Hill on this issue last year.
We also did one of our Innovative Analysis series on the issue of Senate vacancy procedures last year.