No, this is easy to refute with a cursory look at the data.
Nationally, US median household income is 63 K (source: https://www.sentierresearch.com/pressreleases/Sentier_Househ...)
Nationally, the current US median house value according to Zillow (2019) is 229K (source:https://www.zillow.com/home-values/). This includes houses not up for sale.
The median value of houses listed for sale is about 290K, and the median value of houses sold was about 240K. This discrepancy is because higher priced houses languish on the market and cheaper houses sell more quickly, thus there is divergence between the median price of listed houses and the median price of sold houses.
Let's take the midpoint of that and say a household plunged into the housing market should expect to pay 265K. That's a multiple of 3.9. Let's say this household pays 10% down, then their mortgage payments would be about 1400 (use a mortgage calculator) or about 27% of the median household income of about 5.25K/month. This is affordable.
This is the same for specific areas. Take a look at Phoenix metro, the nation's fastest growing area. Median household income in 2017 was about 52K (source: https://www.census.gov/quickfacts/fact/table/phoenixcityariz...)
According to Zillow, median house prices in Phoenix in 2017 was about 200K. (source: https://www.zillow.com/phoenix-az/home-values/)
This is also about a 3.9 ratio.
But now, let's swing over to NYC. Median household income in NYC is higher than Phoenix, but not by that much. It's 61K. (source: https://www.baruch.cuny.edu/nycdata/income-taxes/med_hhold_i...). But the median house price in NYC in 2017 was absurdly high, about 600K (source: https://www.zillow.com/new-york-ny/home-values/). That's a multiple of 10.
So your choice is paying a multiple of 4 versus paying a multiple of 10. No wonder that people are moving out if they value owning their own home.
We can also look at home ownership rates. In the U.S. the home ownership rate is about 64%. In NYC, 30% of the units are owner occupied and 70% are renter occupied (source: https://www1.nyc.gov/assets/hpd/downloads/pdf/about/2017-hvs...). In Phoenix, 53% are owner occupied and 47% are renter occupied (source: https://www.towncharts.com/Arizona/Housing/Phoenix-city-AZ-H...)
Nationally, about 36% of housing units are renter occupied and 64% are owner occupied (source: https://fred.stlouisfed.org/graph/?g=oPyK)
So it's not true that wages are so much lower in the rest of the country that housing is equally unaffordable. Median household income is usually less than 10K higher in the expensive areas, but housing costs are 1/3 to 1/2 of what they are in the high priced areas. That explains much higher home ownership rates outside of the expensive areas.