I do it while watching TV or something. It never seems to stop though. Even better when the kids spill something on the couch or wet the bed and you have to do impromptu laundry in the middle of the non-stop laundry.
Yeah they get immediately stuffed into their corresponding drawers. They rip half them out anyway.
As for when they get older for school... Their shit is getting rolled just like mine. Way easier, more compact, and able to see what's what immediately after opening your drawer. They'll be helping the whole time.