I don't think we can build a robot that takes a pile of crumpled up clothes from the dryer and folds them (reliably without destroying any of them).
Human arms and hands are incredibly intricate. Reproducing their facility with hardware requires a large number of actuators and finicky fine parts. This isn't a software problem. Industry solves it with maintenance schedules.
There's probably nothing in your house that has as many moving parts as a robot needs. Your car maybe, and pretty much all it does is rotate wheels.
That's not the case. I've seen folding robots. They require standardized input, only fold one type of clothing and don't do it reliably.
But you can't buy it because it'll break in about seven days.