You make a common economy error. You are assuming the price of a good or service is defined by its cost. This is only true in very liquid (competitive) markets. Banking is no such market.
You make a perfect case of justifying that the cost of providing the lending service would be higher. However, prices are not defined by cost. They are defined, loosely, by what the market can bear. The cost is a lower limit, but nothing more. Namely, it does not define the price.
For the price of a good or service to approach cost of goods, you need very strong and constant competitive pressure. The banking market, in most countries, is not nearly competitive enough.
It is certainly not the case that cost == price, I agree. Price is determined by supply and demand. But if you change the cost of mortgages, you probably change their supply curve and hence the market clearing price. To argue that raising the cost of mortgages doesn't change the market clearing price is make a pretty strong claim about the shape of supply and demand curves.
You make a perfect case of justifying that the cost of providing the lending service would be higher. However, prices are not defined by cost. They are defined, loosely, by what the market can bear. The cost is a lower limit, but nothing more. Namely, it does not define the price.
For the price of a good or service to approach cost of goods, you need very strong and constant competitive pressure. The banking market, in most countries, is not nearly competitive enough.