I actually do wish Senators were still appointed by Governors, rather than elected by people. The Senate is all about achieving the best of the best, and Americans are too excitable to reliably vote for literally the best people for it. But I wouldn't stop there, if I could.
I wish the only election we, as people, voted in was local representation. Then those local representatives get together to vote for who should go to the state house, then those state house members vote who goes to the state senate (if your state is bicameral). Then those state senators elect state-held positions like Lt. Gov and Governor. Then the governor appoints for the for the federal House, but he/she has to appoint based on a district's political leaning, (so in my State both KC and STL would still have liberal representatives, for example, under a Republican governor within the system I described above). Then the Federal House group for each state would get together to nominate and vote on who should fill (whether re-election of the current Senator or election of one of those representatives, those are the only options) any open Senate seats for their state. If they elect one of their group to be the new Senator, then the Governor has to appoint a new representative federally.
Which makes me need to clear something up. Each level higher up can only appoint from the level below them, so no outsiders:
Local voted by people.
State House chosen by local leaders from among them.
State Senate chosen by State House from among their group.
And so on...
Then the Senate votes for who will be in all federal positions (President/Vice President, Secretaries of whatever, Ambassadors, etc).
We do it this way with the goal of getting the best, smartest person available who works with other people well and can represent us well. Then we avoid people electing bad leaders based on stupid things like speeches, good burns, the color of their skin, their gender, or any other non relevant detail and instead have leaders elected by their peers for their abilities of the mind and nothing else.
What you’re describing here is essentially the electoral system of the Soviet Union or the PRC 😄.
The flaw with that system is that you will end up with a more elitist government than the current US one and a far more authoritarian executive office.