A few things to note:
a) Not an American in Europe: an American in the Netherlands. Visa programs are set by countries themselves so the experience in Ireland won't be the same as an expat in the Netherlands. There are certainly some countries that are more welcoming
In the Netherlands you can't just come over unless you're on an expat visa. And "Integrating" requires five years of continuous employment. The problem being if you get laid off (as I was) and blind sided you basically get shipped home.
And getting citizenship may mean renouncing your US citizenship. Again depends on the country, some will let you have two citizenships (although not all will)
b) There is a HUGE difference between current climate in Europe for immigration and five to ten years ago. Many new restrictions were added after the economic crisis. Even more restrictions were added when all the syrian refugees started showing up. With such a large influx of migrants (and rampant xenophobia in some countries) many governments are making the bar for a non-refugee much higher.