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.

The fundamental question is, do people have a right to free speech on the web?

The web is nearly entirely privately owned, which makes answering this question difficult.

On one hand, the web is where we do 90% of our communication these days and losing that right seems like losing most of the first amendment.

I’m convinceable either way. Did telephone companies have a right to censor land line speech? Should they? Should ISPs be able to censor? Should cloudflair? AWS? It seems like industries like ISPs should be regulated to be “dumb pipes”. But where social networks fall is less clear.