The "public" town square as you've described it has literally never existed. You're asking to return to a time that simply never happened. You talk about strawmen, but you've invented from whole cloth a concept from history that simply did not exist. In classic conservative fashion, you want to "go back" to some idealized era of history that didn't in any way look the way your rose colored glasses seem to tell you it did, and you
completely throw out the outright racist, sexist attitudes that pervaded literally everything happening in prior centuries.
Just logistically, how did these "public" town squares function? Were they periodic meetings? Did people just walk to the center of town and start shouting? Who spent their time in these town squares, when they could be working/providing for their family? Since they didn't actually exist in history, there's nowhere I can look this up, and I'm curious about what you think happened historically.
Setting aside this made-up "town square" concept for a moment, you really seem to want to allow some speech, but to not allow other speech, and that is really the problem here.
If you want to allow all speech, then you necessarily must allow for speech that (successfully) calls for the "cancelling" of people who speak, as well.
In other words, either you support Twitter's ability to express itself through the banning some users for their speech (which it does exceedingly sparingly to begin with, people are not banned for ideas, but for specific expressions of those ideas), or you only selectively support free speech. You don't get to have it both ways.