Well, technically it's not a crazy idea. Like Bandlab's online DAW.

PG Music could have an active Band In A Box somewhere in the server... You log in with your credentials and have a "shell" that resembles BIAB on your phone,.but much simpler, with no content. All the heavy duty is done on the servers and the result is bounced back to the phone in a form of mp3 or other small playable file.

An online version of BIAB with phone interface....
Not sure how high demand for this might be.