Hard times aren't as safe as good times, all around.
Investors get paid to take risks. The less risk you want, the less you get paid, and there is a point at which you're taking so little risk that you get paid less than you lose to moths and rust. During hard times, the level of risk required to get a positive return is higher.
Alice, Bob and Carol come into the bank and each take out a $5000 loan. The bank credits each of their accounts with $5000, but there is still only $5000 in their vault, so now they have 25% reserves. As long as the reserve requirement is below 25%, this is fine. If the reserve requirement was 30%, they couldn't make that many loans.
With a 0% reserve requirement, they could loan your $5000 to a million different people and have 0.000001% reserves and still be allowed because 0.000001% is more than 0%. They could send you away and the bank manager could deposit a dollar and they could make unlimited loans from it. They have no use for your money.