[FromOmelas]

Current wisdom was that higher interest rates would be good for a bank (after all, deposits are sticky). That didn't turn out to be the case for SVB (high concentration of risk, ...) but is more true for a more diversified bank, especially with a lifeline like the BTFP.

More importantly, the actions of the FED after SVB signaled they'll do whatever it takes to keep the system stable.

If a single bank was getting close to your hypothetical scenario, you'd probably see a forced merger. If the majority was at risk, you'd probably see actions to ensure higher margins (such as using reg Q to impose maximum rates on deposits)

[amluto]

In general, higher interest seems good for banks. But I do wonder to what extent high interest rates encourage depositors to move money out of the banking system entirely. Right now, there is no particular limit on the ability of depositors to use those deposits to purchase short-dated T-bills or their money-market equivalents — there’s plenty of T-bill liquidity to go around. (Presumably this results in the banks, on average, holding an equivalent amount less of various agency debt.)

Not doing something along these lines is fairly expensive right now.