Europe isn’t a single country. We have multiple countries where you can create a company in no time, with little capital. And have freedom of movement within the whole EU
I moved to Spain from The Netherlands as a Dutch citizen. It was a lot of paperwork, lots of planning, needed close to €10k in my bank account and needed to get private healthcare with a pretty serious health check. I had to do multiple trips to the national police office and municipalities.
That is not needed when you switch states in the US. You just need to update your address and tax records. You do not needed to show financial means and you do not need private healthcare.
To a certain degree. In the US you can drive to another state thousands of kilometers away and decide to just live there for the rest of your life.