No, because the FDIC would collect higher fees commensurate with the increase in insured deposits. It would reduce profits for banks like SVB which have a large number of uninsured deposits and were able to take advantage of a "fed put".
There are many ways that banks might fail. Most of those are idiosyncratic and unique to the bank's operations.
When the money is spread across multiple institutions most of the risk the FDIC is taking is uncorrelated, therefore costing less to insure.
Quite refreshing compared to the American Capitalism hellscape, though kind of expected because its a national corporation.