You seem to be going to the real cost of housing; there are very complicated feedback loops and if there is a good argument for what should happen in theory I don't know it.
My personal belief is that if you reduce bank lending then they will discover they can't raise the interest rate enough to make up the losses from people borrowing less money. You might reasonably disagree.
Note that in practical terms the way a bank loan works is that a buyer can elect to jump to the front of the queue of buyers by promising some of their future earnings to the bank. Since all buyers have this option, the equilibrium is likely a bank extracts some portion of the future income from all the buyers without changing the ultimate order of the queue (the buyer with the most money is likely the one who can promise the best return to the bank to stay in front). It doesn't really cost the banks anything to create a loan, they just account the money into existence. That factors in.
Given that frame, it seems likely to me that reduced bank lending activity will be to the net benefit of the buyers at maybe some cost to the sellers. Exactly how it shakes out depends on the details of how lending activity is reduced.