The idea is being discussed:
With recovery elusive, a population doddering into old age and perhaps a decade of deflation in prospect, Japan may start mulling the most radical monetary policy of all — the abolition of cash.
Unorthodox, untried and, said one Bank of Tokyo Mitsubishi strategist, “in the realms of economic science fiction”, the recommendation has nevertheless begun floating around Tokyo’s corridors of power and economists have described Japan as particularly suitable as a testing ground.
One policy goal is to open up the option of negative nominal interest rates, perhaps as low as negative four percent. It's worth noting that although you can buy swine placenta drink there, simply by swiping your cell phone, currency in circulation still amounts to 16 percent of gdp.
I don't know if this is a good idea or not, but if anyone could pull-off this "economic science fiction", it would be the Japanese.