The only legal protection they have is not being held liable for the speech of their users. Newspapers don't have that because the writers are on their payroll.
"By actively utilizing technology and manpower to delete notes from its computer bulletin boards on the basis of offensiveness and "bad taste", for example, PRODIGY is clearly making decisions as to content, and such decisions constitute editorial control. (Id.) That such control is not complete and is enforced both as early as the notes arrive and as late as a complaint is made, does not minimize or eviscerate the simple fact that PRODIGY has uniquely arrogated to itself the role of determining what is proper for its members to post and read on its bulletin boards. Based on the foregoing, this Court is compelled to conclude that for the purposes of Plaintiffs' claims in the action, PRODIGY is a publisher rather than a distributor."
[1] http://www.tomwbell.com/NetLaw/Ch04/Stratton.html
Section 230 was written after that court decision. Yet for the law to be consistent its provisions must agree with this reasoning.
So, I understand what you say but Twitter would beg to differ with you.
Also network effects are harder to come by in newspapers. Imagine if there was one newspaper that had 100x the readership of the second most popular one. That'd be considered a threat to democracy.