Ideally they would, which is what happens to some banks in 2008. Unfortunately the banks that stepped in and bought failing banks got very badly punished, because they also inherited a whole bunch of liabilities far beyond the failing bank’s deposits, liabilities the purchasing bank didn’t expect and ultimately cost them substantial amounts of money.

If FDIC wanted another bank to buy SVB and make depositors whole, they would almost certainly also need to guarantee some sort of firewall against any liabilities beyond the deposits. Presumably the purchasing bank would want some ability to pick and choose exactly what bits of SVB it buys, and which liabilities. Leaving the remainder with either the feds, or some shelled out SVB entity. But who’s knows if that’s a path FDIC want to go down.