and folks wonder why banks are so strictly regulated... no, banks are never sitting on too much cash unless they've made a marketing and/or an operational error. most banks are highly levered, meaning they're lending out, say, 10× the cash they hold, so they never "have too much cash on hand". quite the opposite. banks continually lobby regulatory agencies to raise their leverage thresholds so they can lever up even more and rake in more of that sweet, nearly risk-free[0] cash flow.
that they don't raise savings rates is purely out of greed, not necessity. they're also under no competitive pressure to do so, which indicates a malfunctioning market (functioning markets are by definition competitive). and more galling, they charge you hidden fees out the wazoo for the "privilege" of banking in a mine field.
banks are core infrastructure, much like roads and housing. i'd rather go back to a simpler form where banks were only allowed to make money on the spread between lending and savings rates, making them boring and having to compete (with higher savings rates, for example) for your business. all the risk-taking extensions to banking can still exist, just in a separate, firewalled entity with no access to that (nearly) risk-free cash flow.
[0]: risk-free in the finance sense of being free of idiosyncratic risk, not systemic risk.