So I only see two major downsides:
1) I basically I have to verify/transact every "printed" money the moment I get it - preferably using a smartphone - in case someone else has a copy of it and "takes" it first. Copies could be made with any high-resolution camera.
2) If the money travels from A to B to C in paper shape and the digital transaction will be from A to C then A will know that B has done business with C.