To be honest, if banks were the custodian of my cryptocurrencies, I wouldn't mind because the chances of my crypto being lost is going to go down drastically and if it was in an unlikely event got lost, the banks will have sort of insurance that will be in place to take care of the losses.
I don't think it's a nice thing to let the banks hold your cryptocurrencies. The fact that banks are classified under custodian wallets, meaning you do not have the overall control on your wallet because the banks are the ones handling your funds is a big risk already. Your identity is also needed in order to secure your slot in their organization. KYC is very much needed because they claim that they are just avoiding illegal activities such as money laundering.
Another thing is the security banks provide for their consumers. It is weaker compared to the blockchain technology non-custodian platforms offer. Once someone knew your personal information, they could easily access your account and take all your funds. You'll have a hard time recovering the coins/money you've lost because of their slow-paced process. I just like to add that not all banks provide insurance just like what you're expecting.