Should Social Media Companies be Allowed to Moderate Content on their Platforms?

Im all for free speech and our first amendment rights, but I think private companies have the right to ban and censor materials that come across their platform.
The events at the U.S. Capitol on January 6th shocked the country and much of the world. Controversy has continued to rage over the role President Trump's social media comments played in inciting the crowed to violence. Social media companies, such as Twitter and Facebook, decided to ban President Trump, and other individuals that they felt spread misinformation or incited violence, from their platforms. Some have argued these actions violate the first amendment, but this argument is problematic. The first amendment only restricts the government from infringing on an individual's freedom of speech. Twitter and Facebook are private companies that own the platforms on which people post and presumably have the right to ban content they deem objectionable. At present, both federal law and judicial precedent support this view.
In fact, one could argue that no one has freedom of speech at all! A careful reading of the first amendment reveals that it only prohibits the government from restricting an individual's free speech and it says nothing about private companies doing so, nor does it clearly state that people have a right to free speech.
(Interestingly, the fourth amendment is an example of the constitution clearly granting a right, and not merely restricting the government's actions: "the right of people to be secure in their persons, houses...shall not be infringed." Compare that to the text of the first amendment: "Congress shall make no law...abridging the freedom of speech." The fourth amendment states people have a right to something, but the first amendment never says people have a right to free speech, only that Congress cannot restrict it.)
It might be that the only right we have in America regarding freedom of speech is to not have the government restrict it. That interpretation means Twitter and Facebook can do what they want.
However, others argue that current law and judicial interpretation of the first amendment is outdated. They argue that the intent of the first amendment is for individuals to be permitted to practice free speech. Technology has changed the way in which free speech is communicated and the authors of the first amendment could not have anticipated that the real threat to free speech would be from private companies and not from the government.
This debate is not merely driven by support or opposition to President Trump. For instance, the CEO of Twitter, who approved President Trump's ban, recently made a series of tweets in which he expressed concern over the precedent his company had set by banning the president from their platform.
Read the following article and then perform your own research. Should social media companies be allowed to moderate content on their platforms as they see fit or should their ability to moderate content be restricted? Why or why not? If social media companies should be restricted in some way, what would that look like? All of your statements and arguments must be backed up with supporting evidence and you must engage in research beyond the article I have assigned.
Please reach out if you have any questions.
https://www(dot)washingtonpost(dot)com/outlook/2021/01/14/trump-twitter-ban-big-tech-monopoly-private/