Just to offer a counterpoint, as someone who has used the Concierge Service a few times, if something is important enough to require their help I much prefer to call and ensure that my request is understood and that they're working towards the end that I need. The extended wait time are not acceptable but they're a recent issue, apparently brought on by staffing and further compounded by a surge in demand. In the past I have never waited more than a few minutes to get in touch with the Concierge. I expect that when things finally return to normal (I wouldn't expect any time soon) that the phone will be a perfectly serviceable means of communicating with the Concierge.

If I had to speculate as to the why, and not that I agree with this, I believe that AMEX is likely trying to reduce "small asks" that people may be more inclined to send by email.