New York City has more people in it than the 4 most populated metro areas in Italy. Italy has ~3x the population of the state of New York, half the population of the state lives in NYC area.
So they need it more than Italy. You can handle wayyy more traffic without cars on the road than you can with.
The obvious answer is more public transport infrastructure & bike lanes.
If you think population density is an excuse for public transport infrastructure not coping or need for more people owning cars I suggest taking a long hard look at e.g. Japan to have that hypothesis reality-checked.
I'm btw. not saying you did, just reading between the lines.
As I wrote in an earlier reply to parent, NYC hasn't managed to even build ring Metro lines around its city center – since a century!
And that is for one reason and one reason only: not nearly enough (political) pressure from the public to improve public transport infrastructure.
And that in term gets us to the root cause again: the US can't imagine itself without cars.
This is not a critique. It's just an observation that is very plain to see if you grew up in Europe (and possibly many other places, too).
When/if that changes, ever, the above things will just happen naturally.