Bad news: we're actually closer than you'd think to that, considering how many cellular modems on their own are full blown SOC stacks and how far we've gotten into the eSIM camp.

Cell modems are their own SOCs, but are their application processors being used to implement the main functionality of the TV?

Maybe they are, with Android UIs and whatnot? I actually don't have any "smart" TVs (main TV is a 43 inch monitor driven directly by Kodi), so I'm still picturing the car model where there is a separate component that does WAN communications, and the software developers made the system tolerant of it being disconnected (for development ease and also resiliency to failures). But maybe my model is horribly wrong for TVs.