You’re not going to get statesmen that way. You’ll just have more elitist parasites choosing elitist parasites and bypassing the only way to stop that: the people.
Really, do you think “Statesmen” are produced by this present system?
Rather, the Senate HAD Statesmen and subsequent to the 17th the traditions that encouraged them steadily eroded till we have this lot. They get worse, not better.
To paraphrase: With Statesmen like these who needs useless knaves and fools?
To the last comments I will add that the “elitist parasites” you’d get have their job only because they keep the “elitist parasites” in the State legislatures happy.
You know, people whose job prospects aren’t nearly so secure because they aren’t individually so removed from most of their electorate as a US Senator presently is?
The old saying about fooling people applies: it is one thing to fool a large body of strangers (statewide no less) about who you really are but another entirely to fool your peer, the people who actually know you.