We are a big country and regionalism is not quite dead. I would say based upon the aforementioned American cuisine is regional.
Yes, I agree, and I have the privilege of knowing and eating the food of two of the best regional chefs in the US - Tom Douglas and Ruth Bronz.
But if you were to travel randomly throughout the U.S. you could cover the whole country and never get a good meal if you didnt know the few special places to go. Whereas in France and Italy - which also have regional cuisines - you could wander randomly from one third class restaurant to another, and always have great food.
Cajun and BBQ would be American foods though based on earlier French and Spanish influence.