A number of people are now offering paper free services. Companies like BT and Powergen offer a paper free option where they do not send out paper bills. Instead you get billed by email.
The problem is that you do not have a piece of paper to use as a form of identification when you try to open up a bank account.
The requirement for a utility bill is as evidence of address and a number of other items will suffice in lieu such as a council tax bill, credit card statement, income tax notification etc. Although we may eventually get to the stage where none of these are issued in hard copy form, a computer check can usually identify the occupiers at a given address.