The Jira analogy falls a little bit flat, because the information entered into an EMR is often the actual product, not just documentation. Orders entered into the EMR directly affect the outcome of the patient, and errors can be fatal. Having a free-text hand-written system for something like that just seems pretty crazy. It'd be like going to a dev shop where no one used linters or wrote tests and the check for deploying to prod with no rollback option was one (admittedly extremely skilled) guy in the basement signing off after a quick code review.
Two bad things that can happen... one, the order entry procedure on the computer (besides being more time consuming) has usability problems that make it easy to enter the wrong thing accidentally. And an incorrect order looks as official as a correct order. In the old scribble system, where everyone deals with the same physical chart, things that may be a bit more ambiguous/indecipherable are more apparent. Plus, equally importantly, there's more communication between different professionals around the chart. The EMR takes a lot of the ad hoc communication out of the equation. For an example of this in another domain, air traffic controllers used paper "flight strips" to represent current state; initial attempts at computerizing these completely missed that the strips were not only information but also a vehicle for ad hoc communication, and that latter part, critical to work actually being done, was missed in the computer systems.