They absolutely do depend on the premise that getting banned from Twitter isn’t that bad. I’ve made this exact argument here many times before; Twitter doesn’t rise to the level of ubiquity and necessity for us to consider classifying it as a common carrier. Meanwhile I absolutely can see some argument for email getting such a classification.

Any time that we discuss whether or not the government should step in and curtail the actions of a private party, we are explicitly or implicitly balancing the harm of government interference against the harm that such a private action might cause.