Want to end the corrupting influence of money in politics? This is the way to do it. And, as an added bonus, you end up with people from all walks of life in the legislature. There are simply no losers in this scheme - except incumbents and money men, which is why getting this adopted has turned out to be so hard.
Not quite. You forgot about some other people who lose with this scheme. Public funds don't just magically appear, that's tax money you're talking about. That means no matter which raving loony gets elected, you helped. When some David Duke clone manages to win office, you'll have the pleasure of knowing that you spent some of your hard earned cash to fund his election. Taxpayers lose.
A bigger issue is the gatekeeper problem, as in who decides which candidates are eligible for public funding. That likely will be the people already holding office. Think about that, as laws get closer to outlawing private financing altogether. Want to run against the incumbent? He might be one of the people deciding how you'll qualify for campaign money. Want to run a campaign outside the political establishment? Start a new political party? Good luck! You may well find it's illegal to raise money. Public funding of elections is one more step toward consolidating power in backrooms at major party headquarters. The biggest loser will be grassroots politics.