there is one possible way to solve the coordination problem: just stop allowing withdrawals. the chinese figured this out. but you have to limit withdrawals on ALL banks because you bet your ass if one bank gets frozen, everyone will think another one is next and run that one too.
the only time we've rushed a serious contagion before was by instituting a bank holiday and basically putting in 100% deposit insurance. and that was when we had someone in charge whom most people trusted (FDR). biden, yellen, powell aren't so loved.