IIUC "FDIC insurance doesn't cascade into your customers' accounts" is not true in all cases, pass-through deposit insurance is a thing (https://www.fdic.gov/financial-institution-employees-guide-d...).

The problem in the case of Synapse was that they said they were doing that stuff, but were lying. (I think. The details of what happened there are apparently still not public. Also their bank seems to have been doing some sketchy things too.)