Why should there be a limit? What is the purpose of that?
Because without a limit banks have less incentive to avoid risks. They get all of the upside and none (or little) of the risk.
I wonder if having two years of FDIC insurance would work.
The first their would have limited coverage. The second tier can cover all deposits, but will come with stricter liquidity rules.
Then it would be up to depositors to chose to use a bank that has tier one, which will be able to offer better rates and less fees, or tier two which would be more limited in their ability to make money from investments, and therefore would offer less to customers.