LocalLLMs would be useful for low latency local language processing/home control, assuming they ever become fast enough where the 500ms to 1s network latency becomes a dominate factor in having a fluid conversation with a voice assistant. Right now the pauses are unbearable for anything but one way commands (Siri, do something! - 3 seconds later it starts doing the thing...that works but it wouldn't work if Siri needed to ask follow up questions). This is even more important if we consider low latency gaming situations.

Mobile applications are also relevant. An LLM in your car could be used for local intelligence. I'm pretty sure self driving cars use some about of local AI already (although obviously not LLM, and I don't really know how much of their processing is local vs done on a server somewhere).

If models stop advancing at a fast clip, hardware will eventually become fast and cheap enough that running models locally isn't something we think about as being a non-sensical luxury, in the same way that we don't think that rendering graphics locally is a luxury even though remote rendering is possible.