Well, cash hasn't exactly stopped them either. I don't know what the figures are elsewhere, but in the UK around 97% of money is created by private banks making loans, not by the central bank printing notes.
Oh please learn some economics. Bank loans are not new money.
Some TBTF banks have a problem of under-capitalization and may be bailed out with new money, but banks are government's strawmen on this racket.
Bank loans are new money according to The Bank of England
http://www.bankofengland.co.uk/publications/Documents/quarte...
The reason banks get into trouble is because they cannot meet even their tiniest obligations in actual currency. In a cashless society this will not be a problem, just unlimited digital money creation.