>Is it so typically American to eat highly processed foods
Yes.
>Don't you have a vegetable department in the stores?
There are a large number of Americans, especially the poor, for whom the only nearby "grocery stores" are bodegas, convenience stores, minimarts, etc, from which the supply of fresh foods tends to be limited at best. Add to that how spaced out everything in the US is and how poor Americans may not have a car or the free time to drive a considerable distance to a proper grocery store and back and stocking up on anything but the shelf-stable basics can be pretty hard. Take a look at "food desert" maps for more information.
>Here it would also be quite expensive to buy prepackage stuff as one gets peppers, cucumbers, zucchini etc for under 40 cents a piece, a bag of washed fresh spinach is about 1 euro, potatos costs less than 50 cents/kilo
Where I live, in a fairly low cost of living city, prices from a local grocery store start out at $1 apiece for bell peppers for cucumbers, $0.80/pound for potatoes, and $2/pound for apples or broccoli. Increase from there for most other big cities, or for people living in food deserts who have to spend their time getting to a real grocery store if they want anything approaching reasonable prices for fresh stuff.
By contrast, even convenience stores and minimarts will often have processed foods available at a cost low enough to approach those of "real" grocery stores, since canned foods and frozen dinners don't go bad if they're left on the shelves for too long.