If people really wanted to live packed together like a hive of insects, we would not have suburbs and small towns. People live in high density situations because they have (or perceive that they have) no other choice.
Places like NY have extremely high densities of cultural resources and extremely low densities of housing. This doesn't mean people like the housing, it just means people like the cultural aspects.
This begs a big question: why do we pack all of our cultural institutions into a small area? Is it more cost effective? I would have a hard time buying that due to how many restaurants, businesses, etc close in Manhattan for not being able to catch up with rent. I think it's a cyclical issue we see in other areas. Why is Shenzhen the "only" place that manufactures electronics? It is likely a network effect causing this. Factory A can sell to B, C, and D which can all sell a similar fan out. The same likely happens with cultural institutions. Starting a restaurant supply company? Well, you'll look for the place with the most restaurants. Starting a restaurant? Look for the place with the most supply companies. Want to find a place to live? Look for the place that has the best optimization of {Rent, Entertainment, Food, Employment}. For me and many others: this is NYC (actually NJ with a commute to the city).
A bigger follow up question: Does it need to be this way? I don't think it does. Living in Manhattan/Brooklyn/etc is way more expensive than living in the suburbs of NJ even factoring in double taxes and commute. I currently pay $1,500/month in rent for a 1br 1bath. A friend who lives in Brooklyn (with a 15-20 min shorter commute) pays about $3,500/month and needs to pay $300/month in an MTA card while also spending way more on groceries and cost of living stuff than I do.
If you owned your residence in a suburb even with taxes my guess is it becomes much more financially beneficial even if you need a car. If we got a little smarter and built trains, street cars, buses, subways, etc in suburban areas with sprawl we may not even need cars for most Americans.
If we have separate single-family dwellings than the damage fires and poor maintenance can cause are limited (blast radius). We can, as a society, gradually "roll-forward" new standards in electrical codes / eco friendly by renovating homes as people move.
The only reason we don't have a single family home to give to everyone who wants one is because we haven't built them. Once everything is said and done though the cost of building an apartment complex in NYC is not much cheaper once you factor in the huge fees for doing any sort of construction in NYC.
I personally think that if we, as a country, decided to build walkable small towns that were interconnected by fast moving and reliable public transit and forced businesses who could work remotely to do so many people would much rather live there than in the city.
Urban societies have existed for millennia, and before cars, people weren't all riding around on horses to accomplish their daily life. Personal transport was the exception, not the rule.
People in the US think that stroads and roads and cars are the only way to live, because we have outlawed other forms of living. Our lack of low-car city designs isn't because people don't want them, or because they aren't conducive to modern life, they simply don't exist because they have been banned from the marketplace.