Do you think that Hillary! would have been appointed by the NY legislature? Besides eliminating the problem of campaign finance, you'd also eliminate the "carpetbagger" issue of waltzing into a state and claiming the seat.
The biggest reason for states appointing senators is that it completes the tie between the people, the states, and the federal government. The state legislatures define the congressional districts, but the people vote for state legislators along different district boundaries. If people take care of their states first, the state legislatures would appoint senators more in line with the people's wishes. You would also see less of a tendancy for senators to endorse state money being sent to Washington only to be doled back out to states with strings attached.
-PJ