This is my biggest complaint of Linux being where bare metal should. For whatever reason my car takes multiple seconds on startup between starting the music and registering my inputs to lower volume or pause. Older cars didn't have that problem.
That said, cars have 12v batteries. If the pi was better (again another gripe, choose better products not just what everyone else uses) you could put the thing to sleep. Even a good low power Linux machine can go years off one of those (quick math says like 100 years, so negligible draw). Or you could cut yourself off if the level gets below a threshold for too long. Plenty of solutions.