Do you really think putting it out as mortgages would lock the money up for a shorter duration? SVB had a reasonable amount of liquidity for normal stresses. They'd gotten close to breaching their regulatory cushion for spare capital which was why they were trying to recapitalize.
However once the VCs panicked started a bank run, they folded. Just like literally any bank would. ~45b of net withdrawals in a single day is going to cause any bank significant trouble.