I think banks make their money not on interest rates but on various fees and overheads: each person getting a mortgage pays 10K (or more) to the bank right away. That is huge upfront money in addition to the interest rate.

Same with late fees etc. Huge business.

Why would they? For the longest time retail banks weren’t allowed to, and investment banks get risk free money via management and brokerage fees. All investing returns involve risk, it depends on your time horizon.