materials. Therefore, in a free market, the lower interest rate would allow people to afford a more expensive i.e bigger/nicer home, but would not have much effect on the cost of a home per square foot. The limitation on supply, zoning laws, and people buying bigger homes has lead to an increase in price much more than the lower interest rates.
Otherwise competition among builders would keep the price low.
If all you are claiming is that lower interest rates allow people to buy bigger homes and the cost of the median large home is increased over the cost of smaller homes, then nobody's going to argue with that. I think there are other factors besides simply building bigger homes.
I apologize in advance if this was not intelligent enough for you.