Well, the good news is that the vast majority of those monitors and TVs need a WIFI connection, which is optional to set up. However, unfortunately, we're on the cusp of devices having their own permanent mobile phone network connection. Rozzie can confirm.
All they need is flip a few bytes in the software and all newly sold screens only work if they're registered with an active, unbanned and non-anonymous account and were online in the last 12 hours.
And then you won't just get randomly banned from Facebook or Google with no human support staff to talk to, you'll also lose access to half your media devices. This is already true for Oculus/Facebook (and probably some others).
> all newly sold screens only work if they're registered
The other side of this pincer movement is to mandate that all devices which access the internet must send a remote attestation of their boot process, to check that you haven't "tampered" with them by installing your own OS or jailbreaking them.