I'm not sure we have to. If you just make a company responsible for what they've posted, then the civil court system will probably figure that out, won't it?
Companies aren't, and should not be, responsible for what other people post on their websites.(See Section 230 prehistory)
But neither is a company liable just because they engage in moderation.
Why not just make a separate court system instead of tying up the existing one? We couldn't call it the Ministry of Truth because it's the US, but maybe Bureau of Truth?
Who is going to pay for these court cases?
Who has the money to draw them our indefinitely?