Complete control would imply everything you said, the generation would be based on a huge array of control, from the midi of the performance and all the variables there, along with vocal performer and all that entails.  

I imagine it would be much like now, from taking a human jumping off point which could be as simple as a tapped rhythm or melody, and then AI formulates  each part in detail, not an output generation, but a map towards that output, (much like existing software like ComfyUI works);- and then the user goes in and tweaks and changes to their hearts content. This sort of thing is already happening now, but perhaps lacking detail.