You'd need massive networking improvements too. Telling someone "try next to the stairs, the cellular signal's better there" is an example I saw yesterday (it was a basement level), and that's not uncommon in my experience. You have both obstacles (underground levels, tunnels, urban canyons, extra thick walls, underwater) and distance (large expanses with no signal in the middle of nowhere); satellites help with the later but not with the former. Local computing with no network dependencies works everywhere, as long as you have power.

Eventually all devices will be powered continuously via radio illumination by The Network itself, more like The Thing than like today's wireless charging <https://en.wikipedia.org/wiki/The_Thing_(listening_device)>

Yes but by removing pretty much all processing on the end device and making it a thin client, you can extend battery life exponentially.

Is it actually the case that local computation on mobile devices is much more expensive than running the radios? I was just the impression that peripherals like the speakers, real radios, and display often burn up much more power than local manipulation of bits.

You are definitely correct ni that the screen takes a bit chunk of the power, but it is my understanding that the cpu is taking the most. This is why you cannot run x86 systems on battery power very efficiently.

Look at it this way. Older laptops on x86 have the same screens as the newer arm based laptops, but the arm laptops have significantly more battery life using the same battery tech. This is definitely a sign that the processor is the biggest user of power in the system.