The big 'but' is that there are so many hidden requirements here. Privacy is a huge concern. Data on patients may not leave the hospital. With the devices we have these days, it is almost impossible to create a near offline system. Almost all devices are connected to "the cloud" in some form or another, making them vulnerable.
The fact that health insurers are grossly incompetent in this aspect does not mean that hospitals should go down to that level.
Another hidden requirement is that this system has to work, always, no matter what happens. Paper notes may not be efficient, or complete. However, you can be pretty sure that while the hospital is still standing, this system works. Making a digital system that is as reliable is a very hard task.
All this will make such a system a huge investment, not only the system itself, but also in training. Balanced against the cost, it is not so evident that this is really an acceptable investment.