It seems to me that in this situation savings accounts would have the nominally negative rate, whereas checking accounts would have a nominal rate of zero. Since inflation affects the real value of both accounts equally, then the checking accounts would have a higher real rate.
Since both accounts are covered by FDIC insurance [0], it seems that the only difference (unless I am missing something) lies in the rate of return, thus ceteris paribus and the checking accounts have a better rate of return compared to savings accounts. Both have real negative rates, so the situation would be an active discouragement to hold the government-managed currency in any form.
Regarding cash holdings, you are right that they are probably a bad idea. However, if numerous banks could potentially experience a crisis beyond the intervention capabilities of the Fed and Federal government, then it would probably be more sensible to move the money into cash and store it in safety deposit boxes, possibly across multiple banks. This to me seems an unlikely scenario, but not necessarily impossible.
Since both accounts are covered by FDIC insurance [0], it seems that the only difference (unless I am missing something) lies in the rate of return, thus ceteris paribus and the checking accounts have a better rate of return compared to savings accounts. Both have real negative rates, so the situation would be an active discouragement to hold the government-managed currency in any form.
Regarding cash holdings, you are right that they are probably a bad idea. However, if numerous banks could potentially experience a crisis beyond the intervention capabilities of the Fed and Federal government, then it would probably be more sensible to move the money into cash and store it in safety deposit boxes, possibly across multiple banks. This to me seems an unlikely scenario, but not necessarily impossible.
[0] https://www.fdic.gov/deposit/covered/