Silicon Valley Bank had nothing wrong with it's business practices other than they were concentrated in one particular industry, and a slowdown in VCs pumping money resulted in them shrinking deposits suddenly. They asked their investors for money, some VCs basically yelled fire in a crowded theatre and boom a 40 year old institution was wiped out in 24 hours.
America has thousands of banks, and the way you would have this work would shrink that to 5. This way of operation would also wipe out every single credit union. Literally none of them have the insane levels of stability necessary to trust with money, if larger accounts are going to be at risk of a bank run.
That 250,000 number hasnt changed in nearly a 100 years. Maybe it isn't what we should be going off of?