I think the privatization of surveillance is much scarier than the privatization of censorship. To escape the latter, I can just visit my local library, whereas the former is growing at such alarming rates that it might just make that impossible very soon. The chilling effects are real.
Imagine if every single law on the books is enforced 100% of the time. No leeway, no margin for discretion.
You underestimate the ability of cultures to self-censor and convince free-thinkers to leave.
Plenty of people in North Korea are afraid to speak out, for fear their neighbors will rat them out. Same goes for speaking against royalty in public in Thailand.
That said, I do think the First Amendment was born out of practicality. Censoring speech, even in the internet age, is not a good growth strategy when your competitors censor less. People will do their best to get to the most free place.
There were never practical limits on 1:1 communication even in the worst dictatorship because you can't have a policeman in every house. The first amendment was always about public discourse.