You're describing the status quo, and even that falls apart a little. There are already exemptions, like businesses being forbidden to discriminate based on "protected class", utility companies cannot refuse service to customers they do not like (as long as those customers pay), emergency rooms cannot refuse service to people they do not like, and so on.

What we have here is a small group of companies exerting quasi-monopoly power; Apple and Google controlling "apps" or Twitter and Facebook controlling "social media". Sure, they have some smaller competitors technically, just like East Germany had some smaller political parties technically.

If it was up to me, I'd change the status quo: Let FAAGT decide if they want to be publishers, no limited liability, or open platforms, limited liability but at the same time they have to agree to Freedom of Speech for all, unless it's criminal speech like incitement to violence, or some narrow additional predefined exemptions such as the option to not allow pornography or nudity or gore.

And then, if Parler fails to moderate their content again and leaves up criminal stuff, it's the job of law enforcement and courts to not only sanction the people who abused Parler to commit these crimes, but also the state to sanction Parler.