There are several types of common carriers. One are transportation companies (including companies that transport electronic communication). The key differentiator between those and social media are that the content is private . So while they have to carry anything, the content of what they are carrying is from one party to another, and the carrier may not even know what it is. So that model shouldn't apply to social…
Online platforms are both communication platforms for private communication and public broadcast platforms like TV and Radio. Just apply the existing laws and regulations to both these aspects. If they don't want any liability, then they should be treated as common carriers who have to be neutral to the content that flows on their platform - let the content producer be liable. Ofcourse, this means anonymous content cannot be allowed.