Good luck using a piece of paper to e-prescribe a medication such that it's shipped to the patient's pharmacy before the patient even shows up. Ditto for lab orders, imaging analytical tools, custom vital tracking with automatic flagging, diagnostic hardware integration, etc. there is lots of stuff in modern doctors offices that would be significantly more difficult on paper.

Not to mention all the issues of paper management and physical security once you have thousands of patient documents scattered around in filing cabinets.