Well, that’s kind of subjective - obviously some cops will have different standards than others.
However, the DOT has regulations specifying the minimum light output of indicator lights. Wikipedia says the figure is 80 to 300 candela. So, the amount of leeway you have depends on how bright the taillights are from the factory. If you buy a cheap car that puts out only 80 candela, you’ll be under the minimum level if only one LED breaks. If you buy an Infiniti FX45 (which has ridiculously bright taillights, in my experience), 73% of the LEDs would have to fail before you’d be in violation of the law.
I think** Absolute**'s answer is pretty close. Most jurisdictions have a minimum distance requirement, that the light is visible, typically I think it’s about 500ft. Still, it’s subjective and you’ll probably get a “fix it” citation, not something most people are going to contest.
I was in the trucking business and one complaint I heard, about LED’s, is that they don’t generate enough heat to melt snow from the lens.
It’s worth pointing out that LEDs don’t fail in the same way that incandescent bulbs do. Once you get past the few that are bad and might fail early on, the rest are going to last a very long time, probably longer than the lifetime of the car.
They also don’t ‘burn’ out, though I imagine you were using the term colloquially.
It’s similar to LCD monitors, which (at least up until recently) were sometimes sold with several bad pixels out of the box. The rest of the screen is fine, and the pixels don’t start to wink out one by one as the monitor ages.
So the most likely case with a car headlight is a panel that goes bad quickly, early on, or goes bad quickly due to some other electrical problem. We’re not going to see a lot of questionable cases where the police have to make a lot of judgement calls on the status of half-bright lights all over the road.