the real problem with household robots is that they are either flimsy toys or dangerous machines, and there's not much in-between. If we were to build a humanoid robot that would just put laundry away (as described in a HN article a few weeks ago), it would need to be strong enough to lift a laundry basket, have advanced control systems to go up and down stairs, and also be safe/reliable/trusted enough not to hurt people or damage property. We can do these things (modulo the trust, probably) but the confluence of all of it gets very expensive very quickly.
People want Rosie from the Jetsons, but the compute power required would be astronomical, the mechanical systems would need maintenance, and there would be real safety concerns.
With LLMs, we've got the wisecracking figured out...
It's not expensive, it's an unsolved problem, the main issue for many years has been the modeling of cloth behavior. They already have a folding robot that means they have solved a significant chunk of it.
But the generalization of behaviors is also a large problem. Pick and place is mostly solved I believe, but translating your housework to pick and place in your apartment is still a bit off.