If 5 million people save 1 minute every day for 200 days a year. Then you have saved 1 minute every day per person, not 5 000 000 * 1 * 200 minutes in total per year.

That kind of math just doesn't work.

Yeah but you don't have to just sit there and twiddle your thumbs while your machine boots. You can just do something else. I'm sure we waste far more time during the day doing other things. We don't necessarily obsess over those types of time inefficiencies. If you wanted to save time you could brush your teeth in the shower etc.