I've worked through this argument several times and abandoned this premise. It would take more effort to bribe so many officials, but the bribes would be much smaller and therefore more difficult to discover. For one thing, there would be 10,000 possible sources of corruption to investigate. I return to the belief that the Congress should have more members not because of the economy of bribery. The economy of scale in the current system makes it unworkable. How can one person represent half a million people living in up to twenty different towns?
The suggestion is ridiculous. It also costs a fortune to run a legitimate campaign against the incumbent. Politicians quickly learn the value of photo ops and speechifying. It gets their names out, and people rarely question the validity of the news story. The challenger has to create these media exposures for himself. This takes time and money, which eliminates many potentially good candidates. He has to convince more than 250,000 people that he is the right person for the job.
If the district contains less people, it is easier to do this. The district is not one of the gerrymandered abortions we currently use, so the people actually have things in common. If the district only has 30,000 people, or 50,000 (my preferred number) then it's much easier to reach them. You'd be surprised how many hands you can shake standing outside Wal-Mart on a Saturday morning. I can do that, even driving my little Chevy and working full time. You can do it, too. Even if our campaigns rely on BS, we have to stand in front of a group of people and smile while we deliver that BS. If we deliver enough BS, our neighbor BilltheDrill might also decide that he can run for the office against both of us.
You cannot properly represent the people when they do not understand the proper processes of government.
As has been known for thousands of years, once the people recognize they have power, they will do all they can to gain riches from the treasury.