I think you have it backwards: one of the benefits of being treated as a "common carrier" is that you aren't responsible for others misusage of your service, since you are required to be open to the public.

Common carriers can't be held criminally liable for what their users do, but they are responsible for the actions of their users in the sense that they need to turn over their records if served a subpoena, and may be legally required to keep certain records.

ISP's are not common carriers and have lobbied for decades to not be treated as common carriers because then they can't do deep packet inspection and they must sell equal service to anyone. If a drug smuggler drops a package in a mailbox the postal service is legally obligated to deliver it and not look inside (assuming it doesn't smell or tick). An ISP finds out someone is sharing their wifi with their neighbors, the ISP can cut service b/c of breach of terms of service.