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.
I have reverse camera connected to SBC with Allwinner H6. It easily saves around 5 seconds compared to Pi (their closed bootloader takes ages to even start loading kernel). I considered early booting the system when opening the door, but really it is fast enough already.
Not too terribly sure, but NXP puts out power consumption numbers and they get pretty low in sleep modes with self refreshed DDR and whatnot. I think it's just something the market hasn't demanded enough. I'm not really a SBC person, usually just uC, where it's trivial to get microamps of sleep current. I'm sure there's an SBC out there that allows for it.
That specific problem sounds like you just have bad software in your car. My car takes a second for the infotainment system to boot, but it doesn't start blaring anything until it's ready to process input.
Interesting design choice. One alternative would be to not send any output to speakers until the controls work? I would wonder what else is wrong that isn't immediately obvious.
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.