I would absolutely communicate with healthcare professionals by email. In fact, I am rather disappointed that I am not already able to do so.
The main benefit of email communication would be that I could have contact with my doctor or other professional about minor issues that do not or should not necessitate a doctor visit. For example, let us imagine that my daughter got a cut that looked angry a few days later. I could email the doctor a picture and ask if it seemed to warrant coming in to see her. This would be much more convenient and much less expensive than going in to urgent care. It would also be better than foregoing a doctor visit and then having to go later when my daughter’s condition worsened.
I think that the more communication we can have with our health care professionals the better. Of course, this might be seen as a bad thing for doctors because it might make more work for them. However, I think that it would be better for overall health care because it would make it more likely that people would see their doctors when they needed to be seen rather than making unnecessary visits or missing on necessary visits.