Voters would become much more interested in who might be elected to the State legislature. Most people today couldn't name their state legislators. That would change.
Even if California appointed Feinstein and Boxer instead of us voting for them, their motivations would be tied to their perception of the willingness of the legislature to send them back, instead of what Hillary! and Terry McAuliff tell them to do. Boxer and Feinstein are currently more focused on the Democrat national bloc politics as dictated from Chappaqua, not Sacramento.
If the legislature keeps sending back Senators that the public disagrees with, grass-roots politics will change the state houses in order for the legislatures to change the Senate.
Furthermore, you would get the big money out of the Senate.
-PJ