Depositors aren't forced to bank with a specific institution. Just like shareholders aren't forced to hold specific shares.
Depositors can pick the banks whose risk profile they prefer.
Depositors can pick the banks whose risk profile they prefer.
Deposits <$250k are FDIC insured. One could say those accounts didn't evaluate the institution that held their funds and didn't really need to. But were they aware of FDIC limits? IMHO, they should have been and likely were.
Depositors >$250k are well aware of FDIC and the risk associated with money in their bank. They really should think about the banks they work with and understand their risk profiles.
Subjective, but I understood how FDIC worked when I opened my first bank account that was no where close to 250k. If it was greater, I would optimize my holdings across different institutions and instruments.
That way small time depositors are also drawn into the ranks of the watchmen of the financial system.
[study on financial literacy from 2022](https://gflec.org/wp-content/uploads/2022/04/TIAA-Institute-...)
In any case, you don't need to be a sophisticated investor as a depositor. Ordinary market participants manage 'flights to quality' just fine, even if they are not sophisticated investors. See https://en.wikipedia.org/wiki/Flight-to-quality
If you want to have a stable financial system, you shouldn't suppress the incentives for people, including depositors, to look for safety. Just the opposite, you should have them sensitive so that they make moves (on the margin) long before danger is serious. Have people move their deposits _before_ it's too late.
Second, what does that really mean? How to evaluate the quality of your bank isn't typically discussed by personal finance teachers, beyond looking at the interest rates and fees.
More seriously, you don't need to do extra due diligence. Just buy insurance for your funds above $250K. Or use standard treasury methods like using institutional insured liquid deposits or sweep accounts.