What makes you believe you'll be able to do so?

Most European countries have surprisingly strict visa requirements - and those apply to Americans as well. Unlike a short holiday trip, you can't just move because you feel like it!

The most likely path for the HN public is probably a "highly-skilled worker" visa, but that requires you to have a sponsoring employer in Europe - which means you won't be getting that fancy American salary. And you'll also have to pay local taxes...

I'm always surprised by how many American tourists have to turn back because they thought they wouldn't need a visa.