Surely there has to be an inverse ratio for an ideal city. I live in a city part-time that is 450 sqmi and 2.8k/sqmi. It is a slow-burn disaster on roids. The transportation plan shows borderline F peak LOS now, with F off-peak residential areas in 20 years. Our sewer system is broken in the middle ring of development. Bloat is the real question. Land is like cheap carbs for a city: it gets fat and dysfunctional. The more people the higher the necessary density.
What bugs me is the definition of "city". People say they live in a city because they work in the MSA, but likely live in a bedroom community. Tokyo, Shanghai, Chicago, I've found everyone identifying as residents of the greater city but can only afford to live in Yakota, Schaumburg, or Guilin. The commute times are unsustainable.
Let's invert the question: what if the whole planet were one metroplex? Now how do you define your place? What differentiates any one geographic location from another? Industrial fringe and CBD both attract daily commutes, so there isn't any real border - no inside and outside. Low density neighborhoods would be a luxury. Commuting infrastructure has an upper limit (Robert Heinlein "The Roads Must Roll" is a wonderful read on this subject). What is a city? We need a better definition than geographic or political boundaries. I know what Rykwert would say. People are being sold a false bill of goods when buying a suburban house or condo with 60 minute commutes to the employment centers.