I can honestly say one of my most productive moments ever was when a design came to me in a dream... And who among us hasn't figured out a bug in the shower after taking a break? Getting good sleep is essential to actually being productive in many endeavors for a few reasons.

Thats what I thought too, people in this thread are giving anecdotal evidence of "being productive in dreams" and then telltelling stories about one or a small handful of problems their mind voluntarily solved while sleeping, that's a very different thing from the eventual capitalistic dream-learning that is the inevitable ending of this research. They'll claim its a utopian dream of "only learn when you want to", and that its totally optional ... then a few renegade companies adopt it and get ahead, then more adopt it, then its mandatory and performance reviewed.