Maybe. But I know when I'm struggling, I worry most about where I'm going to get my next dollar. I don't think we want politicians either getting another job on the side to make ends meet or not concentrating on the task at hand because they are struggling to pay the mortgage.
I would also worry that they could easily be bought off (more than they are now).
"Poor people could still run and would in fact get a pay raise, and rich people may not have to make a sacrifice at all (nothing unusual there; rich people have all sorts of other advantages, which is a separate issue)."
I honestly don't want poor people running my city, state, or country. If you can't manage your own life, how could you possibly manage the lives of thousands of other people effectively? You also don't want people running just for the money and it seems like this is exactly what you would be doing. At least when you are wealthy and running for government, it's a pay cut most of the time. They could be making lots of money elsewhere, but they choose to take the responsibility of running a government.