Well 15 minutes of power on and power off is a bit exaggerated (unless you really misconfigure linux). Normally for most business PC it takes about 1 minute to power on and power off doesn't need to be counted as you can perform this action without you actually there you hit shutdown and it does its thing.
I work on the help desk of a company with over 30,000 employees. It takes at least 5 minutes for our computers to boot up, and >10 minutes is not uncommon.
However the human factor is not factored in even for your 10 minute days of inactivity. At the beginning of the day most people are not at 100%. They will power on the computer, take off their jackets, get some coffee, put their lunches in the kitchen, greet some people, clean their desk up a bit. Also any loss productive during 10 minutes can usually be made up.
At some jobs, you can do that. At others (like mine) you're expected to be ready and working at your start time (there's a small grace period but not 10 minutes) and you can't do that if you're waiting on your computer to boot up, so that 10 minutes would have to be on your own time, coming in 10 minutes before you clock in. That doesn't sound like fun to me.