Should we ask for a move?
Yes, I would second that request although, I would not get too caught up with labels. The whole "Data Science", "Network Science" and other terms, are sitting a bit oddly with my understanding. What else does anyone expect a scientist to do other than work with data? So, independently of whether "we" are scientists or DSP can be considered "Signal Science" (...or whatever), DSP does have a place in the science.
More broad[l]y, could SE sites belong to two categories?
It would definitely increase the DSP.SE exposure but in my mind, I would think of the primary role of a discipline rather when considering its classification...
Why not art?
...yes, DSP definitely contributes to art too...But i am not sure how much help DSP can provide to the suitability of a chord in a scale.
Definitely things that have to do with Psychoacoustics will involve a lot of DSP because DSP is the primary way (in modern times) by which this science obtains objective quantifiable data on which it bases its inferences on. And definitely Psychoacoustics has a lot to do with Music and the perception of sound, but in terms of DSP, this is probably of a secondary nature. It can be resolved by redirection probably.
Hope this helps.