The cost of living has very little to do with the true cost of you living there. In the city, people are willing to pay for convenience, so you can sit in the middle of the transaction and use the added efficiency to increase your profit margin. People that own real estate in a major city are probably making a pretty good return on their investment.

Why would someone pay for convenience? Probably because it's the only affordable way to buy more time. You could pay someone to do your errands for you while you commute. You could fly a helicopter to work everyday instead of driving. Those things are way more expensive than just living in a smaller apartment closer to everything, though. That is what sets the upper bound on how much profit can be extracted from real-estate. If teleportation existed, I'm guessing a lot of urban landlords would lose a lot of money. But it doesn't.

Meanwhile, the suburbs are intrinsically less efficient, but subsidized from the urban revenues. Think about the laws that require phone companies to provide service to rural areas, or the USPS to deliver mail to rural areas, or your taxes buying roads to those rural areas. You, the city dweller, are paying for all of those things.

The TL;DR is that efficiency is not related to the price you pay to live somewhere. It's much more complicated.