Unqualified anonymous internet answer: it's probably too busy.

I believe the brain actually shrinks slightly and channels expand to aid in the flushing.

Anectdata: note how when you're really tired you can't think clearly? Also, how (apparently) if one goes without sleep for too long then the brain suffers irreparable damage.

But what if we evolved sleep before we evolved brains? Might it then have a different benefit and the brain ones came later?