Well, I'm not a lawyer and I didn't sleep at a Holiday Inn last night but if I was, I'd say let's start looking at the laws that give these sites protection under the definition of being platforms and not publishers, laws like the DMCA.
If I post something illegal on Twitter, CEO Jack Dorsey isn't going to go to prison. He'll argue, correctly, that the DMCA protects him because Twitter, as a platform, is not responsible for what its users post.
Except... When Dorsey starts censoring posts that are otherwise perfectly legal, Twitter becomes a de facto publisher and should be held to the same legal standards that other non-platforms are.
Let's start there. If you want the legal protections offered to platforms, you need to get out of the business of censoring legal speech. If you want to censor speech, then prepare to be treated as a publisher, held responsible for everything posted on your site, and lose the protections offered to platforms under the DMCA and other similar legislation.
So who initiates this?
Who starts looking that has standing?
Do you expect Congress to do this? The Executive branch? A private firm or citizen?
I'm not against that outcome or even the means you propose, but I don't see anyone in government willing to take this on.
President Trump tweets about it, and I'm glad to see it brought up, but that's far from doing something.
With one order, he could totally declassify the documents Reps Bob Goodlatte and Devin Nunces have asked for, too. Or fire Sessions, Rosenstein, et al. But he doesn't.
I'd really love to see what you propose, or what I said the President should do, but I just don't see it happening.