I play active basses, and see both sides, batteries are a concern, mainly because they last so long they can be ignored, and die when it's most inopportune.
There would be no issue sending 9 (or18)VDC along with the signal through a TRS cable to power the bass, mic's and DI boxes are fed higher voltages via phantom power the same way. I have often thought about doing it myself.
However, now you would be stuck using the power supply all the time, it's just one more piece of kit to drag along, you'd have to make a battery pack to use with a wireless transmitter, and most importantly, you're adding failure points.
My setups all use a pair of 9v batteries for 18v operation and require removing screws and an access plate to test or change the batteries, so that is a PIA as well.
I think what I'm going to do is to add external test points for checking the batteries without disassembly. For me that seems to be the most workable compromise. If you have easy access (pop out) battery holders, than this is all a non issue.