Yes, but depositors are generally not expected to be sophisticated investors in the context of bank liquidity abd solvency. You don't get a prospectus of the bank itself when you consider opening an account.
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.
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.
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.