> You can always move to new town and start again.

This is accurate. And taken for granted in the US.

Someone once remarked to me: "I think it's cool you can just pick up and go anywhere (on a huge scale)" - They were from the Netherlands.

Well they can move anywhere in the EU, visa free.

Legally, yes. Practically, the EU still has borders and barriers. Language, pension systems, degree equivalence, etc.

Oh and also remember that the EU has freedom of movement for labour, not necessarily people. If you don’t have enough money, you can’t just move to another EU country and hope things work out.

You can as long as it "works out" (i.e. you find a job) within 3 months.