Please no. At its core, a political party is a group of people with common goals banding together to contest elections. Congress and the elections are the public institutions. How people choose to form alliances and contest those elections is a private matter. The only way to make political parties public is to ban private political parties, which should throw up all sorts of red flags in your head.

As for Citizens United, people forget that it's not just about big for-profit companies spending money. Any non-profit group is a corporation. If you and I share a set of political ideas and want to advocate for them, we'd form a non-profit, print pamphlets, run ads, court donors, rinse and repeat. That's freedom at work. It's totally impractical to run such an operation as a single human being. It's totally irresponsible to set up such a group and then legally run it as a single human being. Incorporation is the legal means for people to embark on common projects.