Both the left and the right are unhappy with different aspects of that, but neither wants to face up publicly to the fact that they can't have what they want without cutting the heart out of the First Amendment.
In the former case, one is worried that a company's right to spend their own money and control their own communications (or hire others to communicate on their behalf, which is standard practice), will lead to outsized political influence.
In the latter case, one is concerned that a company's right to control others' use of their product, because they happen to operate a platform that hosts a substantial fraction of the entire public discourse, will lead to outsized political influence.
The private property defense being deployed here is so facile that only a Libertarian could actually believe it. In practice you will not be allowed, for example, to simply buy real estate at a choke point and exercise your private property rights to determine who is allowed to come and go. Public rights of way will eventually be established if you inconvenience the public enough.