As much as I despise what it represents, I believe that if physical currency ceases to exist, some virtual unregulated stand in (such as cryptocurrency) would take place to fill the same role for unmonitored transactions.
Let's call a spade a spade - individuals, organizations, businesses and corrupt officials all want to have a way to have their "special transactions" away from prying eyes, and should one medium be phased out, another shall form, with even less purview from the governments that once issued the currency. That's too much power to give up.