When people get married and think about settling down and maybe having kids, they usually leave high cost of living cities. They want stability, something they can own or rent long term, and usually more space, especially if kids are coming.
Sometimes they move to the suburbs, sometimes across the country.
The only people who stay tend to be rich people who can actually afford to get some space and stability in the city. Even then many of those decide to leave anyway for other reasons, again especially if they want kids.
High cost city centers are basically an extension of college dorms at this point. They are where people go to start their careers or level up, not stay.
This is like saying “study shows that most people in a shopping mall are looking to buy something” then extrapolating some larger conclusion from that.