I worked at a small startup like this once. The boss/founder came from a non-software background, so he was used to expecting everyone in the office by 8 am. The way I explained it to him was "You pay me to think about the software, and solve the problems. I do this not only in the office, I do this in the shower, I do this on the way home, I do this on the way to work. Now, is it more important for me to be thinking about the performance issues we are having while I am drinking my coffee and walking to work, or do you want me to be preoccupied and stressing about being 5 minutes late so you do not yell at me?"
I work at what the owners call a "15-year old startup" and they're very strict about being on time for the office hours. And the reasons you cite (in the shower, while commuting) are among the reasons they pay us salary. We're expected to work a small amount in the evenings and weekends as well as our 40 hours during the week. Our management uses the excuse "Well, it's the tech industry, we all work extra."
Wow that is somewhat surprising. I work at hedge fund, what one might consider a fairly stogy industry, and nobody cares when I come in to work, which is 9 or 10 usually.
That made him think for a bit.