Even then, it does not mean that those malls should allow anyone to sell wares. What it means it allows people to visit without discrimination on basis of legally protected classes like gender and race. YouTube banning a channel does not ban individual from watching videos, it prevents them from uploading videos which is akin to setting up stores.
No, the "public square" designation specifically allows people to do things like come to the mall and set up political protests and whatnot. It's not about _access_ to the mall; it's about speech protections.
Is uploading videos more akin to setting up a store at the mall, or more akin to standing on a soapbox at the mall and giving a political speech? It probably really depends on the video, on whether the video is being monetized, etc.
In particular, I feel there is an important distinction between demonetization and removal here, from an ethical/moral perspective. I can't speak to the legal perspective; I am not a lawyer.
If a mall did that they likely be accused of discrimination. The demonstrators don't demand to be promoted, but simply be treated as anyone else.
That said, I'm not quite sure I understand your point. A speaker in physical space can pretty easily take their speech elsewhere; most obviously to the nearest public street corner. So moving away from a private venue typically does not require anything nearly as drastic as "moving to another state/region".
I'd really like to understand your point and how it applies to both the mall and youtube situations, though, and would appreciate you explaining it if you have the time.
I think there's a difference between "you can speak" and "you can speak in such a way that interested people can hear". The former is not very useful in terms of the right people usually think of as "freedom of speech"; the limiting case of it in the physical world is "you can speak, but only in your own home". So what, if anything, makes for an online version of the public square, where one can go to present speech for consideration by others?
Also, I think online speech is more similar to physical-world speech than you make it out to be. You can't speak online without "imposing" on your hosting provider, their ISP, etc. If you self-host, you "impose" on your own ISP (and probably violate their ToS, if you have a residential connection). You "impose" on your domain registrar. These are all private entities, so you have the same sorts of issues as you allude to for the physical world. And these private entities have been known to restrict the speech of people relying on their services, so this is not a hypothetical risk.
The extent to which someone is entitled to an audience is of course more difficult to judge.
That's the idea those absurd behind "free speech zones" off in a remote corner.
Free speech means free speech in every public space.
Personally I fear the future where the government (or monopoly/oligopoly) in power isolates all opposition in a remote corner where no one can hear.
What if you set up a booth in a shopping mall in the spring of 2016 in California or Massachusetts and gave away pro-Trump stickers? I assure you there are plenty of people out there in both states, many of them likely working on YouTube, who view that as equivalent to your hypothetical. I know a number of them personally.
Trust me, I'm not a fan of the sort of rhetoric you describe. But I also don't like slippery slopes with no guardrails. I expect we'll end up with guardrails here in the end, after a few decades and a bunch of court cases, but it's going to take a while.
Now very likely Youtube plans to do extremely selective enforcement. I'm not sure that over-broad rules with ensuing very selective enforcement, applied only against the powerless and unpopular, is the right direction to head in, but that's what I see going on here.
I think the truth is that big platforms that are conceivably open to anyone eventually become abused, unevenly enforced, and end up being a gamble when it comes to business. YouTube, Google play, Apple's app store and many more are all examples of this.
Also, I couldn't care less whether things are a gamble when it comes to business. I do care about public discourse and control thereof.
Which of these cases is Youtube more like? It's already hard to tell, and it's continuing to change. I expect the legal status of online forums to evolve over the next several decades, just like the legal status of brick-and-mortar spaces has evolved over time.