Yes, regulation and underwriting standards, enforced by Fed and OHFEO, certainly WOULD have made a difference.
When the Fed “prints” money it is in reality making credit more available to banks through the overnight repo system.
If the banks don’t want the credit, i.e. they don’t feel comfortable deploying more capital at the level of acceptable risk, then they won’t.
This typically happens in the middle phases of a recession when everybody knows you’re in it and the Fed has already lowered rates significantly and yet the banks don’t see much increase in lending and investments since they feel conditions are poor credit risk is high. The phrase “pushing on a string” hits the Lexis-Nexis data bases of newpaper business sections for 10-20 months.
Japan’s central bank lowered rates to zero and yet most of the credit it created was NOT deployed inside Japan, but outside.
Also remember that if a central bank targets interest rates, which the Fed does, (as opposed to money supply, which the Fed attempted to do in the 1980’s for a certain period of time), then the Fed is setting the price of money. The quantity that customers take depends on their own business decisions. And if underwriting is lax, they want lots of it since they are under the delusion they can lend out to subprime scum, borrow from Fed or equivalents and make a fat vig, and repeat.
Stricter underwriting and sober credit risk understanding would have resulted in less demand for money. And less inflation.