I currently have a robot washing my clothes, another robot washing my dishes, a third robot vacuuming my floors. Cybernetic systems adjust the temperature in my house and water my lawn. I even have a little robot I keep in the freezer to make ice cubes while I sleep.
So, two answers - 1. folding laundry is a difficult technical challenge. 2. when we get a robot to do that task, we won't call it a robot.
If it has an arm sort of thing doing it, we very well may. If your drying machine had an arm putting clothing up on pins in your backyard vs being a box you dump clothing into, we’d likely call it a robot.
Some people do refer to automatic vacuums and other things that move automatically robots too.
My quick test for a robot would be: does it have at least one appendage-like part performing a task? A washing machine has nothing like that, but a Kuka robot practically is a programmable arm, and Boston Dynamics robots have legs.
Folding laundry (and more generally, manipulating deformable objects) is actually a pretty tough task for robots. So there has been some research on it, and you can find videos of robots doing it (very slowly). I guess we'll get there eventually, but right now even if it's possible, it's not at a level of speed, robustness and cost where it makes sense.
Because folding laundry is extremely difficult for robots, easy for humans and people are not willing to pay much money or give up much space for a laundry folding robot.
So, two answers - 1. folding laundry is a difficult technical challenge. 2. when we get a robot to do that task, we won't call it a robot.