I think there's a basic error in this approach. It assumes that government can and will run better with "big money" taken out of campaigning. But there's a lot of money given to campaigns for several reasons. The first is that, as Citizens United confirmed, money is speech, and spending money to support a cause or a candidate is at the heart of political expression.
The second reason is perhaps even more basic. When government is huge and has their fingers in every pie, it creates a great deal of motivation to influence those fingers. Campaign contributions are merely a form of lobbying, and lobbying has a standard message: subsidize me and cut my taxes and regulations, but burden my competitors and enemies with taxes and regulations, if not ban them outright.
If you really want to "get money out of politics," you need to (as much as possible) get politics out of the economy. (Ideologues will always lobby, and that's fine, because it's the crony capitalism and pay-to-play aspects that are most objectionable.) Which, of course, is not what many reformers want to do. Until they do, they are basically advocating spreading sugar around their picnic blanket, and then complaining about all the ants.