Understanding that lending institutions are typically held to higher standards of risk management, compliance, and reporting, why do we not see more banks offer "loss leader" programs on the lending side when central bank interest rates go up? Or to put another way, if I were a mid-sized regional bank with big dreams of challenging Chase for the #1 spot, it would seem that the fastest way for me to do so would be to start offering conventional mortgages at 3% during a period of increasing federal funds rates. Yes, in the short run it would limit my ability to make slightly more "guaranteed" profit and might slow down reserve growth (since I also wouldn't be able to offer the highest savings account rates,) but in the mid-to-long-term it seems like it would dramatically increase my customer base and put me on better footing to compete with larger players when things returned to a more "normal" time. Instead, we only really see this kind of competition on the savings side with some small banks offering significantly higher returns on savings accounts.
Is it really all risk aversion, or is there something more fundamental at play?