Trump threatens to 'close' down social media platforms

I think this is going to be a discussion thread that is almost inevitably going to be a shitshow, but anyway:

There are people who advocate the idea that private companies should be compelled to distribute hate speech, dangerously factually incorrect information and harassment under the concept that free speech is should be applied universally rather than just to government. I don't agree, I think it's a vast over-reach and almost unachievable to have both perfect free speech on these platforms and actually run them as a viable business.

But let's lay that aside, those people who make the argument claim to be adhering to an even stronger dedication to free speech. Surely, it's clear here that having the actual head of the US government threatening to shut down private companies for how they choose to manage their platforms is a far more disturbing and direct threat against free speech even in the narrowest sense.

If companies are going to self-moderate their platforms then they should not receive any kind of legal protection from user-generated content. I wholly believe companies have every right to dictate what is on their platform but they cannot have it both ways. If you can afford to moderate content you disagree with, you can do so for illegal content as well.

If I own a store and someone injures themselves on the premises I am held liable for that. I did not force that person to enter the store but the benefits of having a store outweighed the risks. Why should internet companies receive special treatment? They should be 100% liable for what happens on their "premises" if they are going to take the risk of allowing user-generated content.