Remove government from politics. I mean that. When government interferes in electoral politics, a sense of illegitimacy hangs over the entire process. Then who cares? Do I want to wear an I VOTED button? No. Even more, when I give money to a political campaign, I do not want the campaign to report the donation. That transaction is private.
Progressives appear to hold that unfettered politics are inherently corrupt, since money and power are inherently corrupt. Untidiness and honesty can actually coexist quite comfortably, as free-for-all politics creates a lot of checks on deceit. For all its ugliness, the last year or two of American politics demonstrates at least that much.
All of these arguments imply that to clean up campaign finance, you have to clean up regulatory regimes. To clean up regulatory regimes, you have to eliminate the ability of business interests to interfere with regulatory processes for their own benefit.