There was a video I saw recently, in which a shirt is placed on a carefully cut and reattached piece of cardboard. The cardboard folds in the means of the correct way of folding the shirt. With a few deft moves of the cardboard, the shirt is perfectly, professionally folded. This is endlessly repeatable if you have a large pile of shirts.
This could be further automated. Remote manipulators could retrieve a shirt from a pile of clothing, and using a camera, orient it onto the cardboard. Remote manipulators can easily manipulate the cardboard, especially because it is the exact same procedure every time, something robots are inherently good at.
If I replace the cardboard with, say, jointed steel plates, perhaps coated with chrome for that lovely shiny look that people like, I can also throw in an ironing step between the placement and folding steps. The shirts would come out crisp, fresh, and folded. The iron would, upon completion of the placement step, lower into place, and move around the shirt until the camera determines that there are no wrinkles in the shirt, and then withdraw. While not in use, the water lever in the iron would be examined, and if deficient, refilled.
I would like to include a pants-folding machine too, but I worry that machine vision is not yet good enough to distinguish between shirts and pants, and that applying the procedures of one to the other may damage that article of clothing.