AT&T first replaced the SIM card (and, of course, updated the IMEI in their mobile switch provisioning), and that restored service for a few minutes before the problem returned.
I erased all data and setting on the iPhone, set it up as a new iPhone, and still had the problem.
Apple then replaced the entire iPhone, and that restored service for a few minutes. Again the "Call Failed" problem returned.
When I was unable to make the calls, any calls to my cell phone would go to an AT&T Treatment Recording, but if my phone were completely powered off, those calls would have gone to voicemail.
I found through testing that if I turned off VoLTE calling, switching it to "Data Only," then I could make calls. But with LTE for "Voice and Data" turned on, I could not make calls.
Eventually, a dedicated AT&T store representative worked his way through many call transfers to a technician who removed the "news you can use 911 TTY" SoC Code from my cellular line. When they removed this feature, I was again able to make VoLTE calls.
