American regional cultures are almost as diverse as European ones.
Not even close. Almost every European country has it's own language (sometimes more than one), and often times regional dialects within countries aren't even mutually intelligible.
In Europe, the differences in traditions and expectations for how to act are massive, with different stories, different educational systems and different political systems. Half of Europe even lived in a different economic universe with the Soviet union just up until 40 years ago. Many European peoples still retain traditional crafts and lifestyles - it's not "quaint little villages", it's a living heritage that it takes both specialized skill and understanding to maintain.
Spain is its own cultural universe spanning the globe, with media that never touches the English-speaking world; Albania and others have been Muslim-majority for 500 years (to say nothing of Turkey); Russia borders Finland in the West and Japan in the East. I could go on but I really think you're vastly under-estimating how different European countries are from each other, and exaggerating the differences between American states.
That's not to say that America doesn't contain diverse cultures, but it's your minority cultures within and across states that provide the flavor. But put succinctly: do think Minnesota is to South Carolina what Denmark is to Slovenia?