> 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. ... it seems likely to me that reduced bank lending activity will be to the net benefit of the buyers

I agree with the first sentence, but not the second. Reducing a bank's ability to lend is similar to creating a price floor. It will certainly drive up interest rates, and this will effect each party differently.

Banks: Even though banks will make more money on each individual loan, banks will make less loans overall and it will be a net negative.

Home Owners: Obviously it will hurt home owners as the value of their home will decrease in proportion to the interest rate.

Home Buyers with Capital: The effect on home buyers is more complex. Some, that already have capital and do not heavily rely on mortgages will do better, as the value of the home decreases. The higher interest rates don't effect them as they don't need to take out loans.

Home Buyers w/o Capital: These folks would do worse. The buyers with capital will blunt the effect of higher interest rates. So even though home values would decrease, the decrease will be slightly less than it would otherwise be because those that don't require loans will be unaffected. Thus the total cost of purchasing a home with a large mortgage would increase.

Conclusion: Slowing lending will hurt home owners, banks, and those without much money. It may help people who are already cash rich. It will likely exacerbate inequality, not help it.