The CAP in Europe subsidizes more traditional farming and farming produce, not corn + hormone beef.

Also there are all sorts of local legislation that limit the extent to which crap food can be passed as real food: a lot of what can be sold as "cheese" in America can't be sold as "fromage" in France and similarly a "sausage" in Britain has a very strict definition of what can go into it (the crap stuff is called a "banger" since BY LAW it can't be called a "sausage").

A lot of the bad practices would be just as cost-saving to do in Europe as in the US, it's just that the legislation is way tighter and to some level (depending on the country) consumers are much more demanding (plus also due to the legislation, producers can't just name the fake stuff the same as the real stuff).

The impression I have from talking to Americans is that to eat good food in the US you need to really make an effort, whilst in Europe for most things comparativelly higher quality ingredients are widespread (often the default), easy to find it and there are quite a lot of restrictions on what producers can put in it (or how it's farmed or raised).