Quality sleep is very important for long term productivity.
Anecdotally, lot of people need to 'wind down' after finishing work, so that they get a good sleep; hence the sleep-work-personal ordering.
On a related point, is it bad to set out to shortchange 'work' by giving them your least productive hours? Wouldn't it be better to try negotiate a 6 hour working day with them, on the basis that you weren't going to be productive for the last 2 hours, anyway?