There isn't much left of the free Internet anyway. Search engines no longer work, all discussion forums are ranked/censored by interest groups, mail delivery is between large entities. Maybe we need an alternative set of root servers for a free Internet.
Inbound mail on the other hand — notably, the OG form of Internet identification — is very achievable for a stick in the mud to set up.
Losing one’s Gmail account would likely have very little impact on one’s ability to send mail, but no longer being able to receive mail at a given address can be devastating. Set up your own domain!