I think this may well be what happens. Eugene Volokh is pretty well respected and it’s a good article, but I also think that it misses some distinctions, misstates the issue with social media platforms, and is bad policy. Maybe because it’s a portion of a law review article he wrote.
For example, the shopping mall in Pruneyard wasn’t requiring that shoppers agree to specific terms of service before entering. That distinction raises a question of whether social media is truly “open to the public at large” in the same sense of a shopping mall. By publishing the terms of service in advance a social media company not only makes users aware of who/what messages or activities are welcome, they also set user expectations for what users are going to be exposed to on the platform.
The issue is absolutely not that social media companies are refusing to host particular viewpoints, that’s ludicrous. There are conservatives all over Facebook and the fact that they’re less prevalent on Twitter has not been because they’ve been banned. The actual issue is asymmetrical application of those terms of service.
So if what what he’s advocating is to address application of published terms of service then what you’re really talking about is who has the ability to define what is obscene (something that the government is historically awful at.) Taking that power away from those companies has the potential to render the TOS completely unenforceable. At that point, you may end up with some guy in a Sonic the Hedgehog costume helicoptering his 10” dong on your little girl’s Twitter feed. OR alternatively, you leave the definition of obscenity up to the platforms and you’ve essentially changed nothing.