I think the argument that private business is going to be the death of free speech is a strawman argument of the right. Typically this demographic goes out of its way to ensure a healthy free market with little obstructions.
However they seem to lack the technical experience to launch a (successful and secure) competing social network of their own. So instead of achieving technological parity and becoming valid competition, they instead aim to impose regulations on the entire industry. It's ironic and disappointing.