But there are also the unintended consequences: people buy things they can't actually afford, like you said, and people begin to qualify for buying homes as investment vehicles, which really screws with things.
So I'm not smart enough to figure that one out.
But does it actually have that effect? Once everyone is using mortgages, everyone is back in the same place as before mortgages.
To put it more concretely: before mortgages, houses might average around $100K because the average person simply cannot afford any higher. Once mortgages arrive, houses might spike to $300K, because your average person can afford that mortgage. So while the example family might not have been able to afford the $100K house because they had $80K, a mortgage won't help because now houses are around $300K.
So I don't quite grasp how this would affect rents. That seems to be an orthogonal issue.
I.e. if there are no mortgages, people buy what they can afford and housing prices remain low. If there are mortgages, suddenly house prices skyrocket since buyers can afford vastly higher prices, making mortgages a requirement for owning a home.
A good position to be in if you're a bank; now you get a big slice of all action.