[yifanl]

Imagine if there was one. In the scenario where there was a bank run on anybody, this hypothetical bank would be more reliable than the government itself and would end up storing all the money available and bankrupts literally everybody else.

Such an outcome is undesirable, so this type of bank isn't allowed.

If you meant a bank that is guarenteed to recover money up to a certain amount, standard FDIC protections have you covered.