I've never had a license, so everywhere I've lived I've lived without a car. Living in Chicago without a car was fine, although seeing friends in different parts of the city could take an hour or so. Or you might get stuck in a neighborhood that doesn't have 24 hour El train access. It also is only about one third of the density of Brooklyn and one sixth of the density of Manhattan, so there are only a few areas with the vibrancy that NYC has. I do like Chicago though, except for those winters.
I've spent a ton of time in SF over the past decade working in tech, so while it's not the same as living there, I've on many occasions gotten stranded in Oakland after Bart closing at night (pre-uber). Those cab rides weren't cheap. Same thing has happened to me in Boston.
I at one point had to spend a lot of time in Miami (had some stuff in a datacenter there years ago, also pre-uber) and I remember one night I got stopped by a local resident telling me I definitely shouldn't be walking where I was walking at that time of night (about 10 or 11 pm). I was walking and talking with him and a shooting happened a block away maybe 5 minutes after he stopped me. Having other options besides being on foot would have been great.
I've spent lots of time in Seattle and Los Angeles without a car, and it wasn't terrible, but wasn't great.
Anyway, that's all to say a 24 hour transit system is certainly not a requirement, but it's a great thing to have. New York wouldn't be New York without it.