I think further deregulation would see something similar to what we see in the credit card market, where everyone's mortgage looks like whatever the laws of North Dakota say, and that the poorest homeowners (or "inept", if you prefer) cross-subsidize the richest. Like subprime, the whole thing would be characterized by interest rate jumps and penalties and a whole bad-faith expectation that someone can actually pay it off.
What this implies is that in the absence of regulation, lenders would prefer to issue mortgages that cannot be paid off. I disagree that the main goal of mortgage lenders is to create foreclosures. Lenders lose money on foreclosures, and the more foreclosures a lender has, the less likely it is that the lender will remain in business.
Mortgage brokers make money every time a mortgage loan closes. Mortgage brokers do not provide the funding for the loan, so any loss from a foreclosure is borne by someone else. Thus, a mortgage broker has no incentive whatsoever to worry about whether a borrower can repay the loan.
However, the "someone else" has a strong incentive to police mortgage brokers. Imagine that you are that "someone else," an investor in mortgage loans. If the broker is offering to sell you a loan that has a high probability of default, you do not buy it. And you do not give the broker the benefit of the doubt. On the contrary, you put in place anti-fraud and quality control procedures that are appropriate for dealing with cutthroats.
What people cannot seem to get their minds around about the subprime crisis is that the biggest losers were the big companies that took the credit risk on the loans, not the borrowers. I think that this reflects our deeply-ingrained folk Marxism, which divides the world into villain and victim classes. Our folk Marxism leads us to view low-income and minority home buyers as a victim class and to view corporations as a villain class. What's wrong with that picture is that the villain class wound up incurring the majority of the losses (I was going to say that the villain class wound up taking the losses, but that would be overlooking the fact that taxpayers wound up holding the bag.)
In a deregulated mortgage market, lenders would try to extract as much profit as possible from borrowers. Consumers would have to be wary. They might need to pay independent advisers to evaluate mortgage contracts, or they might have to stick to reliable brand names (think of what Carmax did for used cars). But it is not in the interest of private sector lenders to deliberately make loans that have a high probability of default.