Do you need to ban cash if you simply phase it out of existence? Turn up instant payments, and any notes turned in at banks and to the government get shredded. Look to China and Sweden [2] for foreshadowing of digital currencies and the eventual deprecation of physical notes.

[1] https://www.google.com/search?q=china+cashless

[2] https://www.google.com/search?q=sweden+cashless