I thought I'd weigh in with my opinion, based on my experience in France. This probably would not apply to other nations in the EU, but some of it may be translatable.
Overall, I believe, based on my conversations with friends in the U.S. and comments I've read online, is that most Americans overestimate how difficult it is to become an expat in Europe. Don't get me wrong: there are hurdles; obstacles that may be impassable for some people. But for others they could do it if they want.
Take a couple of administrative hurdles: financial requirements and health care requirements/costs.
To move to France as, for example, a retiree, along with filling out various forms and supplying documentation about who you are, you would need to demonstrate a sufficient level of financial resources. That would be an impossible hurdle for some, but not all. For example, the current required level of income per month is 961.08€ for a retired individual or 1492.08€ for a retired couple living together. Using today's exchange rate from XE.com, that correlates to $1019.87 for an individual and $1583,36 for a couple. That's considerably less than the average monthly U.S. Social Security benefit of $1666.49 for an individual and $2503.83 for a married couple.
It doesn't have to be income if you're an early retiree who is not yet drawing Social Security. If you have the same amount in your savings or retirement account each year (such as a 401(k) or IRA) that would work as well.
And, France groups Social Security, other pension, 401(k) withdrawals and IRA withdrawals all together as pensions, so they're not subject, in most cases, to taxation in France meaning all you would face would be the same U.S. federal tax obligation as you would in the U.S. (but without state taxes since you're not living in a U.S. state). In short, you get the benefit of living in a high-tax/high benefit society, while only needing to pay the more modest taxes in the U.S,, which I would consider a lower tax/lower benefit society.
France also requires those seeking a long-term visa to demonstrate that they have health insurance for a year with coverage roughly comparable to that provided by the French health care system. That's a burden, with costs in the neighborhood of $10,000 for that year, based on figures I've seen.
However, once you're a resident in France for three months, you not only are are able but expected to enroll in the French health care system (referred to as PUMa, la protection universelle maladie, or universal health protection). So, if you can arrange your one-year of health care insurance to be cancellable after, say, 6 months, then the cost burden could be less. This leads to lower health care costs than you would face in the U.S., lower prescription costs, and these costs could be lowered further if you sign up for optional private health coverage (une mutuelle) to cover gaps in French health care. Count on around 90€ to 100€ per person per month if you do that.
Overall, if you don't live in high-cost locations such as Paris, the Riviera, or similar places, chances are quite good that you could live in France for less than the cost of living in the U.S., while enjoying a better quality of life.
That gets me to what I think are the real hurdles facing Americans moving to France: culture shock, distance from family and friends, isolation, and language barriers. None of those should be minimized or underestimated. They're real, and day-to-day represent a serious challenge for expats. If you feel you can handle it, the benefits can be terrific. But anyone considering becoming an expat should honestly weigh their ability to manage these matters. Your happiness and peace of mind depend on it.