Exactly. The US has very few cities proper, and a lot of huge suburbs that sometimes feature a city-like downtown (L.A., Houston), and sometimes don't (most of the Silicon Valley).

The real honest dense US cities, such as NYC, Boston, Philadelphia, Chicago, and a few others, were built large and dense before the advent of the car, and had entrenched public transportation system before 1930s.

Those that were not as lucky got remade for cars in 1930-1960s, and cemented in that state by zoning regulations.

Europe obviously had a large number of dense cities since medieval times. Even small cities in Europe often ended up dense due to land limitations, and the generally relatively high population density. Cities in the US very rarely faced this limitation early enough, with a few natural exceptions like Manhattan or San Francisco.