Existing free speech rights restrict only the government itself from preventing free speech. They do not apply to private parties. For example, you have no obligation to permit religious or political proselytizing within your home or business.
You are proposing not merely the active enforcement of free speech as such, but removing the existing longstanding right of private entities to determine what forms of speech they permit within privately owned venues, simply because some such venues happen to be large and popular.
This same argument was made 200 years ago when newspapers were the dominant mode of mass information exchange. The country decided then that the government ought not to regulate what newspapers must and must not print, and enshrined this in a constitutional amendment.
How is your proposal to regulate what private sector social media companies are required to publish any different in substance than a (clearly unconstitutional) proposal to regulate what private sector newspapers can and cannot publish?