heres my take (and trying to remember from my 35 year old BTec)
the regulator limits voltage to 12v, it doesn't limit current/power.
any devices in the circuit cannot have extra 'power' pushed to them, they will draw what they need (be it 1w or 100w), ohms law dictates they will not draw more current than required.
the generator can provide a maximum power, it does not 'push' this out it has to be drawn, if the combination of devices in the circuit draw more than the max power, the generator will not be able to provide that hence dim lights or burnt out stator.
so in the case of LED's their performance or life is not dependant on the power of the generator (unless they draw more than the max, which is unlikely as one of the main advantages of LED is it gives brighter lights for less power).
so potential problems..
LEDs are not designed to work in reverse bias, so in AC systems (as in most 'indian' derived systems in use) this will shorten the life of the LED as it is expecting DC, this is particularly the case in cheap devices, also the led is effectively working only half the time when the ac voltage is going i the right direction, and even then it is rising and falling and not at a constant 12v.
Ideally leds should be on DC, or at the very least have a rectifier diode in series to protect them.
if an LED fails, it could go short circuit (a bulb would usually go open circuit), this would draw lots of current and potentially damage regulator/wiring/stator unless there is a fuse that blows.
if a regulator fails it would not limit voltage to 12v, this could cause leds (or bulbs) to fail and would draw more current (burnt out wires/stator etc as above).
I hope that helps.. although I appreciate and respect everyones 'lived experience' regarding this
