There are at least two problems with this approach. First, this just makes you a target when you go and retrieve your paper wallet. Secondly, even if you never actually leave the bank with your paper wallet, this means you need to physically go to the bank every time you want to transfer money. But people need to transfer money on a daily basis in order to pay bills, meaning any access to a bitcoin wallet needs to be highly available. A paper wallet stored in a vault isn't.
The counterargument to this is to store a portion of your savings in a paper wallet. That's fine, but it's not what's going to make Bitcoin mainstream, which is what the conversation is about. It needs to become consumer-friendly.