Dear Jean-Luc, I will read and respond more thoroughly later today but I wanted to mention that the situation where AZ-GTI (and others) in AltAz can excel is in EAA (Electronic Assisted Astronomy). With my Nikon D5100 you can capture deep sky pics of short exposure (10-15 secs) at 1000 ISO and live-stack them and have a wonderful experience of almost-real-time seeing of objects you can't see with your eyes. As you mentioned, doing this requires somewhat precise tracking (sufficiently precise to avoid blurry images during the 10-15 secs of the exposure), although movement / rotation between pics is unimportant since the live stacking can correct it.
Jasem mentioned EAA was in the roadmap of Stellarmate. More later, thank you for your response!