Density mattered a little bit early on, but SARS-CoV-2 is so infectious that it gets around no matter what, unless the strictest possible measures (such as the police-enforced lockdowns in parts of Melbourne at the moment, or the earlier reports of Chinese buildings' doors being welded shut) are adopted.
https://www.tandfonline.com/doi/full/10.1080/01944363.2020.1...
Plus all the counter examples where dense places have quickly stopped the spread. What killed NYC was terrible leadership that told people to go out and enjoy social settings, which launched the initial spread, and then people forced to continue in essential jobs where it could continue to spread. Not density.
Downvote all you want, you know I'm right. :-)
Similar for other activities, there are less people at the school games or theater, but the density is the same.
Your conception of Dan our does not match people's actual behavior.
You seem to think that NYC is primarily facie evidence that density is somehow something that can't be overcome when trying to stop spread, but don't even consider other dense places that have not had the same problems. In Italy, rural towns were hit as hard as dense cities.
NYC could have been stopped if the governor and mayor collaborated to institute policies to reduce social contact. Instead they delayed a week later than they should have, and testing failures didn't give them evidence of how far it had already spread, leading to tens of thousands of unnecessary deaths. We are seeing the same phenomenon in rural tourist towns in mountain areas, that had lots of early travelers.
Social contact is the primary cause of spread. And density does not prevent one from limiting their social contact.
So is public transportation.