This is a really interesting way of grouping the States. It's pretty clear that most of us forget that "state" is another term for "country" and that the name, "The United States of America" was at one time to make that clear. When abroad, I have often talked to people who had traveled to the States and had marveled at how different the real country is from their prior conceptions, which seem to be based on depictions of the East Coast, Texas, The South and the West Coast, only. Even for me, sometimes when I say "in America" I might really mean, "on the East Coast" because that's the America that I grew up in and began to understand the world through, which is of course a highly biased and regional view, the likes of which I suspect many slip into unconsciously.
When I was studying abroad I was asked all the time what it was like to live in The States, and I always had to explain how different each state was from even its neighboring states. So I pretty much told everyone that what they were really asking was "whats is it like to live in your region," and that I didn't know what it was like to live in California or Texas (I image that its noticeably different). Its really interesting vising a country where everyone is so similar no matter what city you visit. It would be wired not having that city/state rivalry I'm used to.
I know what you mean. Though everywhere has their regional cultures and rivalries, I think that it's hard to grasp, even for Americans, just how vast the country is. A friend from England once asked me if I knew all the counties in the U.S., which was a reasonable question from his perspective as a lot of people in England are familiar with the English counties and their distinct accents and customs. I don't even know all the counties in my state and I live in a pretty small one.