Aside from the obvious privacy issues, which are definitely the main problems here, it isn't just users that behave differently. I've got several bans on Reddit that were literal bullshit, like saying a fascist Italy should be kicked out of NATO and the EU. Apparently this is "spreading hate", worthy of a permanent ban, despite the fact that both institutions require democratic foundations for their member states. Mods and admins are just as ridiculous, be it out of malice or simply incompetency. And once you're banned, there's nothing you can do. You can try to appeal but those are in almost all cases denied too.

But it also goes very much against the basic principles on what the internet was founded on. If we put some heavy identifiable restrictions onto internet accessibility then that's a very powerful tool of oppression. Maybe you trust you current government enough to handle that, right now. I personally don't. But even then, you never know what the next one will do. Tools of oppression like this, or AI based surveillance, could strangle any sort of meaningful resistance before it even gains the slightest bit of traction. Just look at how many far right governments had been gaining votes or even got into power over the last decade. Do you really trust those people to handle such tools with the needed responsibility?