I found some pages in Why We Sleep that seem to answer your argument, and tried to quote the essence of it:
Early studies demonstrated that shorter sleep amounts predict lower work rate and slow completion speed of basic tasks. That is, sleepy employees are unproductive employees. Sleep-deprived individuals also generate fewer and less accurate solutions to work-relevant problems they are challenged with. [W. B. Webb and C. M. Levy, “Effects of spaced and repeated total sleep deprivation”]
We have since designed more work-relevant tasks to explore the effects of insufficient sleep on employee effort, productivity, and creativity. Creativity is, after all, lauded as the engine of business innovation. Give participants the ability to choose between work tasks of varying effort, from easy (e.g., listening to voice mails) to difficult (e.g., helping design a complex project that requires thoughtful problem solving and creative planning), and you find that those individuals who obtained less sleep in the preceding days are the same people who consistently select less challenging problems. They opt for the easy way out, generating fewer creative solutions in the process. [...]
take the same individuals and repeat this type of experiment twice, once when they have had a full night of sleep and once when they are sleep-deprived, and you see the same effects of laziness caused by a lack of sleep when using each person as their own baseline control. [M. Engle-Friedman and S. Riela, “Self-imposed sleep loss, sleepiness, effort and performance”] [...]
The irony that employees miss is that when you are not getting enough sleep, you work less productively and thus need to work longer to accomplish a goal. [...]
Interestingly, participants in the above studies do not perceive themselves as applying less effort to the work challenge, or being less effective, when they were sleep-deprived, despite both being true. They seemed unaware of their poorer work effort and performance—a theme of subjective misperception of ability when sleep-deprived that we have touched upon previously in this book. Even the simplest daily routines that require slight effort, such as time spent dressing neatly or fashionably for the workplace, have been found to decrease following a night of sleep loss. [M. Engle-Friedman and S. Riela, “Self-imposed sleep loss, sleepiness, effort and performance”] Individuals also like their jobs less when sleep-deprived—perhaps unsurprising considering the mood-depressing influence of sleep deficiency.