...Lucid daydreaming button, anyone? Maybe not lucid if it's the exact same as normal sleep, but I'm sure that if such a thing more exist, you'd be able to adjust exactly how it affects your brain.
Tell that to sleepwalkers!
- Sleep paralysis doesn't properly activate, and someone accidentally transfers the motion of walking into real life. proprioception may pass through to the dream, they might perceive a dream environment that allows them to navigate the real one. (i.e. righting themself from bed, staying upright while walking)
- They aren't fully asleep, but they aren't awake/aware either. I've had my fair share of people telling me that I said or did things after waking up and before immediately going back to sleep, and those are things I don't remember doing at all, probably because they weren't properly recorded in memory because my brain was not fully awake. (Some of these cases could have been DID though.)
Hopefully without having to induce those brainwaves, otherwise you might be able to do it during the day but you wouldn't exactly be conscious. But there's also the question of whether those brainwaves are doing more than just cleaning the brain.
I think some types of learning and memory formation also happen during sleep, right?