Automated laundry folding is working just fine at industrial scale.[1][2]
Chicago Dryer, a century old company in Chicago in a very boring business, is doing quite well at automated folding. Their approach is about 20% AI, 80% clever machinery, and it gets the job done at scale.
Damp laundry fresh from the washer goes in, and folded stacks come out. There's a vision system with some AI finding corners for a robotic grabber. Another vision system decides if items are worn or damaged and should be sent to the reject bin.