> If it begins make decisions based on what it prefers content wise it would lose a common carrier status

It can't lose what it never had to begin with. Information services post Section 230 have 0 obligation to be "neutral". You should read the law instead of listening to Internet commentators' fantasies and wishlists of "neutrality" and "censorship makes you a publisher". This is all bullcrap.

There is no legal basis for this. Facebook and Twitter are explicitly permitted to amplify or suppress whatever content they wish.

Maybe there should be!

I disagree!

Even if their algorithms threaten to destabilize society by amplification? Bear in mind these platforms come with many forms of moderation already.

So I believe we're mostly talking about a spectrum of what mechanisms there are and their consequences. Ie. is it OK for the entire planet to bully anyone in public until they lose everything? This is actually hard to prevent, if no mechanisms to do so are in place, while communication is as "free" as possible.

Ultimately, if a platform is big enough that its policies have society-destabilizing consequences, I would much prefer to see it broken up than reined in. Benevolent dictators are still dictators.