I am under the impression that we can no longer go to Canada without a passport.

:(

Edit: Since June 2009.

You can't go to Mexico without a passport either. You can't come back without one, anyway.

The US Gov does now issue passport cards which are a form of national ID card that allows citizens back in at international LAND borders. You should ask for one when you apply for your passport; they're nice to carry in your pocket when you're abroad and the full passport is safely locked away.

If memory serves, if you don't have a passport you can go to Mexico, you just can't get back into the U.S.

This notion of equivalence is a very interesting concept.

The US is is geographically larger than Europe, has a comparable number of people, and is arguably as diverse.

Yes, it looks like we speak the same language, but the diversity in "American" is at least as broad as the difference between the middle of "American" and "received English". (Yes, I'm aware that there's a lot of diversity in UK English.)

Yes, Americans mostly watch the same TV, but our exports and castoffs are not unknown in Europe.

America is not as lingusitically diverse as Europe. The difference between 2 American english accents might be similar to the difference between 2 English accents, but there are dozens of languages in europe. You're comparing the whole of the US to one part of EU.