Earlier quoted context omitted.
The milk quality in the US is fine, it's just different. Each carton has been pasteurized differently, then homogenized, fortified, and contains milk from thousands of cows. There are lots of other differences that affect flavor, mouthfeel, aroma. We may also use different cows, environment, etc.
US Milk also tends to be rather old by the time it reaches consumers, with ~2 weeks being surprisingly common. That has several implications which alter it’s taste. Of course this varies a lot based on the store and product.
Unless most people in Europe are buying direct from the dairies, I can't imagine it's appreciably faster. Even then, I grew up having milk delivered direct from the dairy and definitely don't notice any difference between what I grew up with and what I typically buy in the grocery store.
I would guess most of the flavor difference comes from pasteurization differences, since Ultra High Temperature pasteurization appears to be the norm over there.