Imagine a world where this splitting is normal.

If SVB depositors had split their deposits up and stored them at other banks, other banks depositors would have done the same and split their deposits up - and stored some of them at SVB. So from FDIC's perspective, the total amount of deposits at every bank (and so the risk they take as an insurer) after this splitting is the same.

FDIC insurance limited to 250k and a banking system where everybody splits their deposits up into 250k/bank is the same risk profile for FDIC as unlimited FDIC insurance and no splitting up of accounts, assuming the same deposit distribution between banks.