They're not actually living cheaply - just in poverty. Different thing altogether.
They can't do that in the suburbs because there's hardly anything for rent there and they don't have the credit score to buy anything.
My reasoning is as follows:
-Real estate per unit area is more expensive in the city - that's a given.
-Groceries are 30-50% more expensive because again - real estate is as well and that pushes up the price of everything. On top of that you have logistics to deal with, as you need that truck to reach the store somehow.
Sure, in the suburbs you have to drive everywhere and maintain your property, but there's financial flexibility in that - you don't need the newest, most gas guzzling car or to renovate the whole place every 7 years or so.
All the fathers of 4+ children that I know are in agreement that they wouldn't be able to afford having such a huge family in the city.
Whoever thought it's cheaper to live in the city must be childless.