Interestingly the list of some of the richest people capable of destroying such an institution would likely be highly correlated with the banks that can handle it. As it turns out the Fed's existence is due to such rich people desiring the ability to crush the mom-and-pop banks.
I think the banks that can handle it generally have diverse clientele. SVB had businesses and venture capitalists for clients. When you have a few clients who deposit billions and the relationship turns sour between the bank and some portion of the clientele, well watch out.