This is a very important and socially desirable function that banks fulfil. >I'd be willing to pay a fee to the bank to hold my money for me. You are effectiv

This is a very important and socially desirable function that banks fulfil. >I'd be willing to pay a fee to the bank to hold my money for me. You are effectively doing this already (twice). Perhaps your bank charges you a yearly fee for the account in the likes of $10/year, but you're also "paying" by not investing the money yourself, of course, the bank has many lending opportunities that you have not so you might not be capable of doing so. But the point still stands.