It's not really PWM, rather it's multiplexing of displays. I won't go over the advantages of multiplexing in detail here, but it's not power efficiency, rather it's a reduction in cost and complexity of drive components. It's possible to use a few cheap parts to drive a 4-digit LED display (32 segments) with only 12 port pins (on a single sided PCB if necessary).
Most of this kind of product will be using an 8-bit processor rather than some. 32 bit thing, and usually at a relatively low clock frequency such as 4 or 8 MHz. They will not be equipped with a hardware display controller generally, so an ISR will do the work. If there are other things that are high priority then the display digit brightness might be visibly modulated in brightness due to jitter in multiplexing - some level of that would be deemed to be acceptable if not entirely imperceptible. Same thing with flicker in the display. Even so the micro might be spending more than 20% of its bandwidth just controlling the display. Faster clock would mean more power consumption of the micro, more EMI and more cost. For an 8 digit display muxed at 200Hz a new digit must be handled every 600usec or so, +/- 30 usec (that would be a pretty high quality display for an application without vibration). If there is a lot of vibration maybe 5x faster.
Although a designer could propose using, say, a small FPGA to totally eliminate all timing constraints and a 6-layer board to deal with the EMI, that would likely be their final act at a consumer product company. The attitude is that a 5 cent reduction in cost would be sufficient to hire another engineer.
Digital LED mains powered clocks are a special case, and some use a clever biplexing scheme powering the display from an unregulated centre-tapped transformer secondary, so the mux frequency is tied to the mains frequency.
The DIM pin is used for PWM dimming from a control signal:
Connect a logic-level PWM signal to this pin to enable/disable the power MOSFET and reduce the average light output of the LED array. Logic high = output on, logic low - output off.
So if you connect a 50% PWM signal to the dim pin, the led connected to the driver is dimmed to 50%.
The VINS pin is used to detect PMW dimming on the Voltage input:
Adding an external input diode and using the internal VINS comparator allows the LM3406 family to sense and respond to dimming that is done by PWM of the input voltage. This method is also referred to as "Two-Wire Dimming", and a typical application circuit is shown in . If the VINS pin voltage falls 70% below the VIN pin voltage, the LM3406 family disables the internal power FET and shuts off the current to the LED array. The support circuitry (driver, bandgap, VCC) remains active in order to minimize the time needed to the turn the LED back on when the VINS pin voltage rises and exceeds 70% of VIN. This minimizes the response time needed to turn the LED array back on.
It uses a diode and a capacitor to smooth the input, and allow it to dim that way. See 8.11 for details.
If you want to take a steady but variable voltage input, and dim the led by the range of the input, you would need a circuit to measure the voltage, and produce a PWM signal to the DIM pin. Any common microcontroller should do.
Best Answer
The term you need to search on is Flicker Fusion Threshold Quoting from part of the wiki article, we have this:
You need to think not only about what the eye can directly perceive, but possible stroboscopic effects