Ok so I got this idea not while showering, but because I’m very high. The story does come from my bathroom though! I have a night light in my bathroom, and I was looking at the night light as I turned off the bathroom light. I’m a big nerd so I remembered that the things that detect light levels are actually diodes wired in reverse. I thought it would be funny to make it flicker by reflecting the light back on the diode, but it didn’t work. That’s when I had this realization
Duty cycle does not refer to the frequency of the flicker.
The frequency on a PWM light doesn’t change, it’s the same for the full range of control. What that frequency is, is determined by the controller generating the PWM signal, not the light.
PWM can be done at different frequencies. Cheap PWM controllers can only manage lower frequencies, those are the kind you notice and have trouble with in pictures. Good ones will run at frequencies so high, the fact they aren’t actually on continuously, will only matter in extremely high speed photography.
This is because a PWM controller can achieve the same reduction in brightness at any frequency. What matters is the fraction of time that the LED is lit each pulse. If you run the system at 1000Hz, half brightness means the flicker is 1000Hz, because you are sending 1000 pulses that are 0.5 milliseconds long. 75% brightness would mean the pulses are 0.75 milliseconds, but the number of pulses, and thus the frequency, is still 1000Hz. The flicker is the same.
Even at 99% brightness/duty cycle, a PWM light is still blinking at whatever frequency the controller is running at. Only at 100% does it not flicker, as 100% duty cycle means the controller simply keeps the light on continuously.
No matter what LED you use, they don’t usually care what the frequency is, nor what duty cycle you are at.
I’m not sure what you mean by motors running best at a given duty cycle, either. Sure, there is an efficiency peak, but the whole point of PWM is to be able to run something at any duty cycle you desire (resulting in the desired brightness for lights, RPMs for motors).