It seems to me the gold analogy is more applicable when storing BTC than the cash one. I might be OK storing my gold with some institutions, especially ones with a proven track record and insurance policy, but other than those few institutions, I'd probably opt for a fire proof safe (a safe rated to protect the amount of money stored).

If one were to use BTC to store vast sums of money, you can store your BTC with a traditional bank. Simply generate a wallet offline on new hardware with a relatively secure USB bootable OS, write the keys down on a piece of old fashioned paper (use carbon paper and store the copy, destroying the original) and cover with some sort of tamper proof seal. Lock inside a lead box and then put it in a safety deposit box.