Ask HN: At what point should a site be run as a 'public carrier'?

I've seen quite a few people say this about Google, Facebook, YouTube and Amazon recently, and I definitely see where they're coming from. They're large corporations who have a huge influence on what people can do online and their recent censorship attempts may be hurting a lot of people. But then I wonder... what size does a site or service have to be before it should be regulated like a utility? Does it have to have a monopoly in its market? Because that's technically not true of any of the big social media sites, but might be true of much smaller ones in specific niches. If there's exactly one forum dedicated to the Virtual Boy on the internet, should that be regulated? Is it marketshare in general? If so, what sort of level would be needed for a site to qualify for the status? 90%? 70%? 50%? Maybe 20 or 30%? Does the importance of the service have any effect? Email is one of the most important parts of your internet life, so should any site offering email accounts be regulated in a way that stops them closing email accounts for activities the account did elsewhere on their network? What's the practical point where a site or service goes from 'entirely private, can do whatever they want' to 'the government should step in and regulate them'?