The cultural differences between US states exist, but they are NOTHING compared to the cultural differences between european states. Why? because these states don't have centuries of independent histories and different languages and literatures and tradition.
Many of our states are roughly equivalent in size to your countries and I'd argue each has it's own unique culture. Texas, for example, is vastly different from Maryland. And that's in many ways: accent, racial composition (+ level of racism), foods, culture, hobbies, government, etc, etc. -- Florida has alot of Cuban influence -- New Mexico/California has alot of Mexican influence. And so on.
Sure, US states are big compared to european countries, some of them even in term of population (california, at 39 or so millions is comparable to a mid-sized european country). But the cultural diversity that you are talking about to me seems more comparable to the regional diversity within european countries such as italy, the UK or spain, which have mutually incomprehensible dialects/languages, completely different regional cuisines, and in some cases even some level of legal autonomy (spain, germany, UK) somewhat comparable to what US states enjoy.
Americans are very mobile: they move from one state to another to study, work, marry, etc
Says who? Most people never relocate after their first job/marriage. They at best would experience two states, their birth state and their death state. Over 50% never leave the state they grew up in: http://www.pewsocialtrends.org/2008/12/17/who-moves-who-stays-put-wheres-home/
I don't consider that "highly mobile" --
This is fairly obvious to anyone who knows a little about both continents, but if you want a citation, how about this one: http://www.acco.be/download/nl/10987314/file/ (from 2008).
In the for-
mer EU15, only about 0.1% of the working age popu-
lation changes its country of residence in a given
year. Conversely, in the US, about 3% of the working
age population moves to a different state every year,
So by this measure, americans are 20 times more mobile inter-state than europeans are inter-country.
unless they're in the army where they get shuffled around alot from base to base. And that's why language differences don't matter much -- because no one really knows anything outside of their home state anyways.
It's interesting that you mention the army. The policy in italy back when there was the draft was to send people to different parts of the country for military service, to help spread a common italian language and culture, because a lot of people never even traveled outside their region, let alone move there to live and work. That, together with national TV, is what has brought some level of linguistic and cultural unification to Italy in recent decades.