In Toyota, at least, the traction battery is completely disconnected (via a relay) when the car is off. The 12V battery is needed to power anything on the 12V system up until the car starts-- that includes the car's computer, which is what (after doing all its self-checks and whatnot) activates that relay and connects the traction battery to everything else in the car.
The traction battery isn't always connected probably mostly for safety reasons (having 400-someodd volts energized across the whole car even when it doesn't need it isn't great), but that also keeps it from getting excessively drained if something in the car malfunctions. It's pretty cheap to replace a 12V lead-acid battery if it's overdischarged after you left the lights on... the big hybrid battery, not so much.
This had me worried the first few times it happened. Then I found out it is a warning to mechanics/tow truck drivers/first responders that the high voltage system is energized.
It is only on if the car is turned off and parked and the high voltage system has turned on to charge the 12V battery. When you're driving or just have turned on the car while parked, the light goes off.
So the only occasion the light might be annoying is if you're taking a nap in the car at night. And then you could just throw a towel on top of it.
You expect to have the high voltage system energized when driving, otherwise the car wouldn't go anywhere. There would be no purpose for this light to go on.
The light is specifically to indicate that the high voltage system is on when the car is parked. It's a safety warning for that situation.
https://www.caranddriver.com/features/a38537243/electric-car...
There's a lot of Tier 3 supplier…stuff…in a car that was architected for 1978 and has never had a thorough re-think, because the profit margin is like nothing.
There's also a legal requirement that "marker lights and such" still work (presumably, also power locks and such) after a prime mover failure. Basically, if the engine quits, you should still be able to signal, get over, turn your 4-ways on, etc.
The easiest solution is to just put a lead acid 12V battery in the car for that. Lithium, in particular, is a problem below freezing because you can't safely charge it, whereas lead doesn't have that problem.
Some EVs like Tesla now use a separate lithium ion 12v battery that should last forever, instead of a lead acid 12v battery with a limited life span.
My mild hybrid Audi is the same way. Gas engine, 48v accessory belt run battery, and that 48v battery works in tandem with a small 12v battery for the low voltage system.