he only way I could ever see it being secure is if they don't actually allow customers to withdraw cryptocurrency directly, which would make it almost useless. The banks would then have full control over how, where and when you can spend those funds. That would only bolster the argument about how you need to be in control of your own funds to see any tangible benefits.
Your statement reminds me about this news :
Mastercard Wins Patent for Managing Fractional Reserves of Blockchain CurrencyNow they join us
I doubt this about this part. Custodial wallet/storage defeats the purpose of Bitcoin, it's no different from storing your fiat or goods (e.g. gold, jewelry) to banks.