Yep, as PJ O'Rourke once noted, when buying and selling are legislated, the first thing to be bought and sold are legislators.
Here's the solution:
We have a lottery. Everyone's in it. No opt out.
Every couple of years we draw names. There's a national lottery, a state lottery, one for the county, one for the city, one for the school district, each drawing on a pool of residents of the jurisdiction.
The prize? The names drawn have to serve in the legislature, county board, city council, or school board.
The grand prize? President of the United States.
I don't see how it would be any worse than the system we have set up now. Yeah, you might get the grease monkey down at the garage for President, but what the heck? He might turn out all right.