And yet in Detroit, the price of rent has increased while occupancy rates, incomes and population have decreased. This leads me to believe that the rising prices of rent on average in all cities in the first world is not actually a supply and demand issue. When the price for a mortgage is far above what the average person can afford, land prices start having little bearing on rent, and the reverse happens: rent prices start having a bearing on land prices.

Taking Cleveland for example, despite there being a massive surplus of housing units as you say, the average price of rent is 1123$, while the average household income is of only 26179$. This means that the average household pays 51% (!!) of their income into housing in recent years, while there is a surplus of housing.

I don't understand how this can be stated as supply and demand. It seems to me that rent simply increases so as to saturate the budget of the lower class, regardless of supply.

I would also observe that in most cities the average price of housing as a share of average income is steadily rising. This leads me to believe that what is actually happening is that prices of rent are increasing synchronously,