When all of the money is in one bank, the fees it would need to charge to insure the same deposits is much more.

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.

Because they want depositors to spread their deposits around and not concentrate them at any one institution.