I want clean clothes, I don't need something to clean them the way I would clean them. I am willing to buy clothes that are robot cleaning compatible.
I like machine assisted dish cleaning so much, all of the dishes we own are "dishwasher safe" except for a couple wine glasses. They aren't all labeled dishwasher safe, but in those rare cases when the dishwasher destroyed something, I made sure not to buy another dish with that weakness.
Likewise, all of the clothing I use on a regular basis have survived trips through the washer and dryer.
For me, a complete laundry system would take the clothes out of the hamper, wash and dry them, and put them away. In order to put the clothes away, the robot would need to know where they are supposed to go and how to prepare them for storage. I am not afraid of RFID tags, but if I were, there are many other options for creating labels a robot can read.
Folding clothes isn't hard once the clothing is identified, flattened and positioned. The robot readable labels take care of the identification. In exchange for something else doing the work, I am not adverse to having ferrous rings sown into key points, so the system can magnetically grab those points to spread out and align the garment in the folding station. I am not adverse to having clothes rolled up, if that turns out to be easier.
I don't require that a robot adapt to my garage sale dressers. I just need the right clothes in the morning. There are many pick and place technologies. If for some reason it is easier for the cleaning system to deal with cartridges, I can live with that. The cleaning system can load an underwear cartridge. The transport system can load the cartridge into my dresser replacement. Then the dresser replacement can dispense underwear as needed.