That's a ridiculous argument: Banks started being a thing at the end of the Middle Ages. The Great Depression and the Great Recession were not caused by banks emerging, nor by people putting their savings in them.

Not emerging. Just being themselves with all their schemes and an economy dependent on them. A distrust of banks and their schemes at a national level might have reduced their ability to cause those problems. On top of the smaller stuff such as them delaying deposits or withdrawing stuff for bogus reasons.

Putting your savings under the mattress instead of in a bank account wouldn't have prevented the Great Recession. It was caused risky mortgages (debts, not savings) being sold as low risk from bank to bank, and then defaulting.

Putting your savings under the mattress instead of in a bank account wouldn't have prevented the Great Depression either.

The only thing it would have accomplished is making your savings easier to steal.

Storing gold or other valuables instead of Gederal Reserve notes for sale or bartering wouldn't have helped during Great Depression? I havent heard the angle that there was nothing to barter with on top if worthless dollars.