Sleep has magical properties. One of them is that it provides an uninterrupted (hopefully) period of time where ideas and knowledge can take their raw form. They frolic and play, and mesh to form something amazing.
A period of work is then needed to realise those consolidated ideas into something concrete.
One assumption is required though: the work-to-sleep and sleep-to-work transition is managed well.
Alain de Botton once opined (tweeted) that, "Insomnia is a glamorous term for 'thoughts you forgot to have in the day.'"
I'd continue, adding that morning grogginess is the remnant of thoughts trying to exit the subconscious pipeline (and prematurely terminated).
I think those times should be treated as precious. We should actively seek to optimise this time in accordance with our goals , instead of falling asleep to the droning of a late-night sitcom and being jarred awake by the piercing ring of an alarm clock.
Without the bridges, you live on an island. --- Footnotes:
 - Say, if your goal were to increase the depth of your relationship with your spouse, then that time could be spent "exploring". If your goal were to solve really hard mathematical problems, it would be a great time to focus your thoughts on visualising the various processes of mathematical proof