So you're basically implying that private companies shouldn't have a right to moderate content or ban users on their websites without a court order? I don't see how this would be fundamentally different from, for example, requiring newspapers to publish every letter their receive irregardless of their editorial stance.

The real problem is that the market is dominated by a couple of huge companies that have disproportionate power and can pretty much do whatever they want without the risk of losing significant numbers of users. I don't see how legally requiring them to be content neutral can fix that, even if Twitter can't just remove your posts or ban you I'm sure they'll manage to find legal ways to make your content virtually invisible if they want to without directly removing it.