And yet in most European countries there's a clear path to citizenship.
US is a popular destination because people are after money, not because it's good for immigration. Ask for all the H1Bs that risk being deported for being laid off, even after living many years over there.
Legal clarity and strict limits are not mutually exclusive. Nor do many European politicians pepper their speeches with "nation of immigrants" and "diversity is our strength", and when a mere million refugees came from the Middle East (to be fair, that is on top of all the non-European migrants already in Europe), that was a "crisis", and caused a significant rightward shift in EU politics.
For comparison, the US takes in almost 2 million legal immigrants per year (on a population of 333 million vs. EUs 446 million), plus however many illegal ones, and there is nothing like a "sanctuary city" in Europe.
Taking in a refugees is quite different to taking in a migrant who passes all your immigrations tests. Refugees need more social services, housing, healthcare etc.
Also, that number of refugees was on top of normal migration, making comparisons difficult.
The EU takes around 2 million immigrants from outside the EU per year as far as I can tell. I don’t know hot many move with the EU, it’s a lot.
US is a popular destination because people are after money, not because it's good for immigration. Ask for all the H1Bs that risk being deported for being laid off, even after living many years over there.