On the other hand, all of your inherent values of a city center can be said to be caused by higher population density. Food and recreation spots will be opened

On the other hand, all of your inherent values of a city center can be said to be caused by higher population density. Food and recreation spots will be opened close to where people live. Jobs are variable in terms of location, but there's certainly an advantage to moving close to population centers--at the very least, access to a vast workforce. My point is not really to argue that the opposite is true, rather that you can make an argument either way, whether higher demand leads to higher density or higher density leads to higher demand. There are certainly low density urban centers that no one wants to live in despite their proximity to jobs, food, and recreation.