It's an interesting concept but the timing is probably too early. If more people had reliable low latency gigabit or ideally 10gbit throughput, then it might start to approach feasibility. There's other blockers too, but that springs to mind immediately. It's cool to imagine a planet wide neural network interconnected with fiber - the nervous system of a planetary intelligence. But perhaps mushrooms do that already (…
If you run a local model at a good pace, you're emitting tokens at, what, 60 tokens/sec? That's, very roughly, 300 bytes/sec. You can get that speed with dialup from the 80's! And when it takes a half second just to ingest the input tokens (to get to the part where you start generating the reply), you're not gonna care about even a crazy 250ms latency.
Unless you think that the model should be downloaded on-the-fly in response to a user request, there's zero reason for an LLM to need any sort of fast connection.