Berlin's is probably the only major example I can think of a city growing due to actual growth opportunities, but then again Germany is also a much healthier economy than most of Europe.
The US on the other hand doesn't have a primary city in the same manner that most of Europe has - the US economy is pretty decentralized across multiple hub cities (Bay Area, Los Angeles, San Diego, DC, NYC, Boston, Chicago, Phoenix, Atlanta, Dallas, Houston, Denver, Seattle) the same way Germany is (Munich, Frankfurt, Berlin, Hamburg)
This is a MASSIVE assumption to have. The language barrier you brought up has a massive impact for example, along with other smaller intricacies (eg. Taxes, Drivers License, Immigration depending on your nationality, bureaucratic experience, etc). Moving from Paris to Berlin or Oulu to Varna isn't some walk in the park.
And several states don't have primary city effect either (eg. CA, TX, OH, FL, NC), and bureaucratic norms in most cases within the 50 states are normalized for individual cases.
Also helps that Berlin has had a pretty stagnant population for ~70 years and still 20% under its peak in WWII
https://en.m.wikipedia.org/wiki/Berlin_population_statistics
> Substantial population loss in some of the nation’s largest and most vibrant cities was the primary reason 2021 was the slowest year of population growth in U.S. history, new Census data shows.
> Although some of the fastest growing regions in the country continued to boom, the gains were nearly erased by stark losses last year in counties that encompass the New York, Los Angeles and San Francisco metropolitan areas.
> The pandemic played a role, as the number of people dying rose substantially and many Americans left cities for smaller places. But experts say that skyrocketing housing costs were also to blame, and that some of the changes are a continuation of fundamental shifts in American demographics that began before the pandemic, such as the steadily falling birthrate and steep drop in immigration.
As you correctly point out, there's an equilibrium between cost of living and the advantages large cities are offering. Here in Berlin we are starting to feel the pressure hard, but it is still much cheaper than the other big European cities, and thus growing by 200k a year.