I only found out about https://www.rabbit.tech/research today and, to be honest, I still don't fully understand its scope. But reading your lines, I think rabbit's approach could be how a local AI based home automation system could work.
I've gone into a frenzy of home automation this week-end, right after seeing the demo video of this "LAM" from Rabbit, thinking about the potential for software there.
Connected a few home cameras and two lights to an LLM, and made a few purchases.
The worst expensive offender being a tiny camera controlled RC Crawler[1]. The idea would for it to "patrol" my home in my name, with a sassy LLM.