Telcos and isps have terms of service and contractual provisions that allow for common carriage. They clearly and intentionally seek this status to protect themselves from liability rooted in the carriage. (Edit: in exchange for additional duties based on the special relationship formed, if I recall correctly).
Purveyors of coherent speech products derive similar but different immunity from cda section 230, with terms of service that define the relationship as distinctly not content neutral.
Accordingly there is a very differentiated line: the common carriage of goods. Common carriers do it but internet platforms do not.
Stepping back a moment, I stated before that the fee element of common carriage was not present in internet platforms but of course you can buy movies on YouTube so this is not as universally true as I said. On the other hand, try posting a snuff video to YouTube and you will see exactly why it is not a common carrier.
As I understand it, the argument is that if a web site gets to be sufficiently systemically critical to (society? Democracy?) that it should not be allowed to control its speech product. This would go a long way toward making every website 4chan, which is not an optimal outcome.
However I’m curious if I’m missing something. Is the goal here to deny, for example, LinkedIn the ability to constrain you from posting pornography? Or to constrain stack overflow from allowing you to post poor quality answers?