In your system, standard store hours have become a random regional fluctuation instead of a strictly maintained standard. I still need to maintain timezone information, but I ALSO need to do math in my head to figure out if it is an appropriate time to go to a certain kind of store.
You're making an assumption of a standard time of day when stuff's open (I agree, 11:00 is a reasonable assumption). I can, however, make that same assumption. In your travel model, the traveler must know the timezone (and work with assumptions from there). In my mode, the traveler would need to know the “standard daytime hour” and work with assumptions from there.
So, both require one piece of info when traveling, but a single timezone wins out when synchronising.
There is huge variation in these sorts of things worldwide. See, for example, http://www.spanish-town-guides.com/Opening_Hours.htm
Either way, you have to adjust something. Right now, you adjust your known time difference (i.e., change the clock, either by knowing the difference or by asking someone local). With that proposal, you would adjust the known opening times.