The problem with that argument is that there's no such thing as a "public square" on the internet. Everything on the internet is controlled by a private company in some manner or another. Whether you're talking about DNS, cloud hosting, ISPs, CDNs, or CAs there are always going to be some number of privately controlled intermediaries with the means to censor your speech.

For some of these entities, such as CDNs with enough infrastructure to stand up against large-scale DDOS attacks, there may only be a small number of viable options. What happens if all of those companies collectively decide to censor someone? You've effectively created a corporate oligarchy with the power to decide what sort of speech is and isn't allowed on the internet.

Now again, maybe we're not quite at that point yet (after all, the Daily Stormer did eventually find a CDN that would take them), but we may very well be getting close. You also have to consider that even without a true oligopoly; there's still a chilling effect created when a large percentage of the internet's major infrastructure providers collectively decide to censor certain speech on the basis of ideology.

At what point do you believe freedom of speech outweighs freedom of association? We've already decided freedom from racial discrimination trumps freedom of association, so it's not like this sort of thing would be entirely without precedent.