> or access is tied directly to your physical identity to access the site).
This is what is inevitably going to happen. There will be some kind of service provider (probably one of Apple, Google, Microsoft, Amazon) who will verify who you are via official documents such as passport and driving license. When you sign up to a smaller company's service they'll check with the providers to see if you're a genuine person and if so then they'll let you join, if not you'll be blocked. You might be able to use the forum with an anonymous name but the company will always know who you are and if you use your account to spam or abuse people you'll get blacklisted and reported to the police. Any service that doesn't implement the model will be an unusable hell hole of bots and spam.
The internet will splinter into two and you'll have the "verified net" and the "unverified net" with the latter basically becoming a second dark web. To be honest, I think this will probably be a good thing. I think the vast majority of people will spend most of their time on the verified net, which will actually be a more pleasant place to be because people won't be able to get away with what they can now without real consequences in physical reality.
That being said there are plenty of ways it could go wrong - if those accounts get hacked and the owner of the account can't prove it then we could see innocent people going to jail. Or state actors could hack the accounts of citizens they see as problematic and frame them. But all that stuff could happen today anyway - the verification or lack there of doesn't make that much difference but does substantially reduce the use of bots.