Except the Tesla should be able to detect a failed inverter instantly. How would the conventional 12v battery failing cause a loss of engine power, and yet continue running the touchscreen and hazard lights for half an hour?
Lights and touch screens will still mostly work on half their normal voltage, but the propulsion control system is fairly conservative. Rightly so. Trying to keep going on flickering power could cause the control DSPs to behave erratically.
Indeed, you could imagine the system being able to give an earlier warning for this class of failure. Perhaps they'll be able to add it in a future software update.
I've had this exact scenario happen on one of my previous cars. The alternator was somehow overcharging the battery. At some point, the battery acid would basically be boiling over (the battery case was physically bulging out), and no longer function at its job of carrying power to the rest of the electronics in the car. The throttle could no longer operate, so the car just stopped moving, spontaneously in the middle of the road I was driving on. No battery sensor would detect this as there was no voltage drop before the battery stopped functioning, and I could still run the radio and headlights for a couple minutes even though the car couldn't be moved. Replacing the battery didn't fix anything (the first shop I took it to didn't realize the battery wasn't the issue since the alternator was putting out power), replacing the alternator did.
It should be able to see that it was overcharging. Too high a voltage(>14 or 15 volts for a conventional 12V lead acid battery) or too high an amperage would indicate overcharging.
It's tricky. You don't necessarily have to exceed the voltage range that would normally be seen to overcharge the battery, just fail to regulate the output correctly. It's correct to provide a certain extra voltage/amps when the battery is not fully charged and you turn on headlights and fans; it's not correct to put out that same power 100% of the time.
It's probably possible to build a sensor that tracks all this, but normal cars with the same 12V system don't have that sensor either. If the alternator goes the way mine did, you won't even see a battery indicator on the dash (even though it has such an indicator), you find out about it when your car stops moving in the middle of the road.
