The "problem" being solved is that, even though almost everything pro-audio is now digital, the end points are and always will be analog and the end points can be hard to get power to. There's always going to be guitar pedals and keyboards and Space Echos and beat boxes and the little portable gizmo that the guy built so on. All of those devices source or sink signal that should be at pro levels. Ironically, with all of the attention paid to noise and distrotion, traditionally these devices have been accomodated with little 9V battery powered DI boxes or phantom powered devices that have low headroom and weak drive.
Another reason for using batteries is that they could act as a buffer almost like capacitors in a way [1]. So a noisy 5V USB supply is stepped up to 30V and buffered / stored in the 28.8V pack. And you get a center tap for ground.
Also there is a convenience to batteries and especially ones that can be recharged from USB which is everywhere from your entry table, your laptop, the car, an airplane, etc. I'm not sure your PITA point applies to this idea because, unlike your drum tuner, I'm talking about using NiMH. Being a one-off design it is a PITA to make new packs but presumably they would last a few years (espcially if they live an easy trickle charging life) and I could make them 2-3 at a time.
Here's an example of what one of these battery powered gizmos would look like:

So the cable clamp would have a USB cable and 4 signal cables w/ XLR or TS or whatever. The data port is audio over ethernet. Two dual op amps could make 4 sturdy outputs. Now you can put this thing at the end of a potentially very long cable for a plate reverb or in some industrial application where the power isn't reliable or maybe just connected to your laptop for analyzing gear in the field. There's lot's of uses.
[1] I could be wrong about the batteries being like a buffer because I have not yet devised the circuit to ensure that the batteries are always getting 0.04 C to trickle charge regardless of the load being driven. And I might have to connect the center tap to the SMPS to ensure that the batteries are not discharged unevenly. So it's not crystal clear how well I can isolate the downstream supply from the SMPS which no doubt will be a noisy source. Forturnately it's only 34mA (or maybe I use the 2W SMPS and get 67mA) so chokes in the >10mH range are available.