but it would not work well for me.The following would be completely confusing to me
That seems to be your problem. Perhaps you're unable to wrap your mind around it, because you've never been forced to use it. You're not being instantaneously teleported to random locations around the world, having to figure out in which time zones you're now located...this isn't an episode of Sliders. If you're traveling between NY and WA, you either already know the general times during which businesses are active, or you'd plan accordingly. If not, that is your own fault.
Every single issue you described is just as arbitrary as you proclaim my proposed clock to be. Broadcast stations, whether TV, radio, or otherwise already tailor to local working hours. Staples is open based on local working hours. The solar cycle does not arbitrarily change. The key difference with my proposed clock, which has been validated by a little system called "UTC" if you weren't already aware, is that it assigns 1 time keeping value which never needs to be translated and correlates to the solar cycle. Virtually every major international business already runs on UTC with a 24-hour clock, whether you choose to acknowledge it or not. Localities would actually find it extremely easy to use the same system; it would avoid any mistranslations in delivery times, electronic transactions, etc.
I'm sorry you don't understand. Cheers.