You'd still see the rich in those positions. What poor man could afford to take a job with virtually no pay? Even if they paid for your immediate needs (ie, setup an apartment building with provided meals just for elected officials), you're still going to come out of the deal unemployed with no money to tie you over until you get back on your feet.
It's an interesting thought experiment, but in practice? Pretty much an impossibility. Or rather, it wouldn't make much difference. Heck IIRC the presidency still only pays $200k per year. Now to most of us that's a lot of money, but many CEO's make much (MUCH) more than that, and to just about anybody elected to the presidency recently it's peanuts compared to their existing cash on hand.
For the most part it's bribes and power that attract people to these positions. The bribes are unofficial/off the books so you have to tackle those separately, and the power, well, you could take it away, but at that point the whole reason for them being there is kinda diminished.