well, I take "folding" to mean "putting away". Eg, putting your socks in a drawer (usually balled up together, but I guess you could just toss individuals in there).. hanging up tshirts and sweatshirts, putting away your jeans and workout clothes..
Some kind of organization is ideal, because I often live out of the clean laundry hamper and it's a chore to hunt for stuff every time you need clothes.
When I'm not living with others, this problem goes away. I start out with things in the wardrobe and drawers but as I get distracted by the things I actually want to do I gravitate towards a sort of inbox(clean)/outbox(dirty) 'floordrobe' system. It's surprisingly efficient.
Robots? Assuming you already have 7+ days worth of clothes simply hire a maid to come by once a week.
With a human you never have to worry about software upgrades, charging batteries, or wake up in a cold sweat in fear of your hired help violating Isaac Asimov's laws of robotics.
Automate doesn’t have to mean a machine is handling it. It means you don’t have to handle it. Human automation is a valid tool, in particular for things like housework.
Besides, the original question is totally boring if you allow human automation. Of course I can hire someone to do labour. No one needs that explained to them.
Robots are miserably bad at this, so far.