Sure, but these are multi-million cities. They have amazing public transport.
The issue I see here is assuming that Europe = Paris/Rome/Amsterdam. Probably due to tourism. It makes the impression that whole EU is just amazing and no one needs a car. It can't be further from the truth.
Pretty rich that you are complaining about generalization now where you made the initial statement that the "Car is absolutely essential for driving around small kids no matter the urban density" which doesn't seem to have any limits in scope.
You made a clear assertion about the need for cars, regardless of urban density.
But it turns out that actually urban density is pretty good indicator of reasonable public transport. of _course_ there are black spots, rural england lost its trains in the 60s and busses in the 2000s.
But
The british didn't make the tube for tourism, given that they've not built anything transport wise since the 90s (except the Elizabeth line)
Paris didn't make the metro for tourists, because they are french, they're not going to spend money on dirty tourists who get in the way.
the Netherlands didn't make trams for tourists, they can cycle like the rest of us.