I researched this topic a little as it was related to work I was doing in my PhD 2-3 years ago. I'm mostly going from memory here. I think Kaufman is largely incorrect for skill learning in real-life. Walker et al. (2002) found sleep improved motor skill compared to the same amount of time spent awake, but a similar improvement was found after nightime sleep whether participants learned at 10 am or 10pm.
Walker study: https://www.sciencedirect.com/science/article/pii/S0896627302007468
Possibly, Kauffman based his claim on Robertson's studies wh...
The reference for the Robertson paper is: Brown, R. M., & Robertson, E. M. (2007). Off-line processing: reciprocal interactions between declarative and procedural memories. Journal of Neuroscience, 27(39), 10468-10475.