Sorry, but your assertion that an American can simply come to Europe and work is false. In Germany, like in the UK, you most definitely CANNOT just come over and declare your intention to work. "If you are coming to work in general employment (that is, a job that does not require you to be highly skilled or highly educated), you will need to apply for a residence permit for the purpose of general employment, and you will only be eligible if the position cannot be filled by a worker from the EU/EEA or Switzerland." (from http://www.expatica.com/de/essentials_moving_to/essentials/g...). It's the same in the UK.

Germany _does_ have the "Blue Card", which is similar (at least at the very highest level) to the now discontinued Highly Skilled Migrant Worker / Tier 1 visa in the UK. The Blue Card allows you to work in Germany as long as you have a college degree and make above a certain salary (usually above €45000).

Both of those scenarios are much more involved than the way you described, it however.