According to Wikipedia https://en.wikipedia.org/wiki/Public_utility:

Broadband internet services (both fixed-line and mobile) are increasingly being included within the definition.

As for which things are "truly necessary", that definition is not universal. In The Netherlands, over 90% of consumer banking by now is done over the Internet. That has lead to the closing of over 30% of bank branch offices, with associated cost savings. Those savings would not have been possible had Internet access not been classified as a public utility, because bank access was similarly regulated.