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.

I have struggled with both points of the argument for a while now. In general, I'm inclined to agree with your assessment that this would be a glaring overreach on the side of the feds. It's also apparent that social networks have a tendency to cater massively to one side of the increasingly divided political spectrum, as proven with experiments like Gab. I've always liked the idea of having a Twitter clone that bases their philosophy on the 1st amendment, but in reality, all it did was to attract the polar opposite of the /r/politics subreddit (to put it lightly), rather than to facilitate free and open discourse.

On the other hand, Twitter, Facebook, YouTube et al are undoubtedly massively influential on the public opinion and their corporate position on political topics - Yoel Roth's recent tweets serve as a decent example, showing clearly that this person cannot be an objective "fact checker" - essentially create a public forum where I am not able to exercise my first amendment rights (and, legally speaking, rightfully so). I cannot help but to find this very concerning.

YouTube (despite numerous issues with their interpretation of free speech), for instance, starting linking Wiki articles under videos that cover certain topics or are uploaded by certain channels. Videos by the BBC show a notice that the BBC is a British public broadcast service, simply informing the viewer about the fact that any bias they might encounter can be easily identified (feel free to switch "BBC" with "RT"). I've found that to be a decent middle ground between outright suppressing views by a corporation pretending to be the authority on certain topics and broadcasting everything without any context.

That's the first amendment, not the concept of free speech. The concept of free speech can apply to private and public spaces, just as it can apply to government regulation of speech.

First amendment is what matters.

This is not true, there is a large amount of case law in the US that discusses what is and is not allowed in the context of free speech.