Haven't you just described what Coinbase is trying to do? Become a bank?
Only they are starting with the cryptocurrency wallets and will likely add current accounts and loans later, after they've floated on the stock market and raised a lot of capital.
I'm surprised the existing banking system can't see what is coming.
Looks like Bitwala is doing just that:
https://www.bitwala.com/bitwala-bank-account-coming-soon/In the next few months, we will be building a full-fledged German bank account that will come with a German IBAN, BIC along with a real debit card from MasterCard. Bitwala accounts will be fully regulated by The Federal Financial Supervisory Authority of Germany (BaFin) (current application pending), meaning your funds up to 100,000 will be guaranteed, in our case by the deposit guarantee scheme of German banks.
You will be able to buy and sell cryptocurrencies alongside managing your daily expenses and setting up direct debits.The best of both worlds, all in one place.
The new Bitwala account will come with a debit card that is linked to your account (no more bitcoin prepaid cards!). This means that the balance on your Bitwala account will be immediately available on your Bitwala contactless debit card as well. Having the new card will also mean that you will have much lower fees and higher spending limits. No more top-ups or card loads necessary!
How long before the banks respond in the opposite direction and allow online cryptocurrency wallets linked to your bank acccount?