The estimation wasn't 3 minutes a call, but that each patient would take an average of 3 minutes of time in this communication channel. I imagine most patients wouldn't want to email their doctor every year, and that those that ask too many questions would be directed to appointments. I can think of a handful of times in my life that emailing a doctor/nurse would have been the most efficient use of time. Mostly the questions would revolve around "I'm having these symptoms, should I come in for a visit or should I stay at home."

I've (acting in the role of senior developer) directly addressed support tickets that were generated by user support emails and have even directly communicated with users in phone calls as standard level support. Not at Amazon, Google, or Facebook but in Fortune 500 companies and in B2C.

If you aren't talking to your users, how do you maintain empathy?