Why is PWM used to control LEDs even when they're only used On or Off?
Contrary to initial intuition, it's actually to increase the brightness.
LEDs can be driven at a constant current, or they can be driven with a pulsed current.
With constant current you have to limit the current to a relatively low value - for instance many common small LEDs are limited to a constant current of say 20mA.  That gives good brightness for indication purposes, but it's not that great.
LEDs, when driven with pulsed current, can be driven with a considerably higher current - maybe 5 to 10 times as much, or even more.  That could be say 100mA for what would normally be a 20mA LED.  However, there are restrictions on what the pulses can be - typically with limits on the frequency and duty cycle - maybe as little as 1% duty.
The end result is that the higher current increases the perceived brightness of the LEDs, since more photons are being emitted when they are on, but at the cost of some flicker, which is only really noticed when the LEDs are in motion.

A research group at Ehime University developed a pulse drive control method to make LEDs look twice as bright by leveraging the properties of how people perceive brightness.
The group was led by Masafumi Jinno, an associate professor of Dept of Electrical and Electronic Engineering at Graduate School of Science and Engineering of Ehime University.
When a short-cycle pulse voltage with a frequency of approximately 60Hz is applied to an LED at a duty ratio of about 5%, the LED looks about twice brighter [sic] to human eyes than that driven by a direct voltage, the research group said.
- Nikkei Technology - Human Perception Studied to Double LED Brightness

So you get more perceived brightness from smaller and cheaper LEDs without using more current (often less current) on average than if they were on constant.
The report above goes on to explain the effect in more detail:

There are two principles, the Broca-Sulzer effect and the Talbot-Plateau effect, involved in how human eyes perceive brightness. The Broca-Sulzer effect refers to a phenomenon in which light looks several times brighter to the eye than it actually is when exposed to a spark of light, such as a camera flash.
In addition, the Talbot-Plateau effect is a principle where human eyes repeatedly see flashes and sense the average brightness of the repeated lights. Thus far, &quot;it has been believed that, due to the Talbot-Plateau effect, the brightness perceived by human eyes would not change even if an LED is pulse driven,&quot; Jinno said.
&quot;The Talbot-Plateau effect is a principle found in the days when fluorescent mercury lamps and other light sources driven by a power supply with a longer voltage cycle of about several hundred milliseconds were used,&quot; Jinno said.
Thus, the group decided to drive the LEDs using a power supply with a shorter voltage cycle of about several hundred microseconds. As a result, the group discovered that, when a pulse voltage with a frequency of approximately 60Hz is applied at a duty ratio of about 5%, the impact by the Broca-Sulzer effect becomes greater than that of the Talbot-Plateau effect so that the light emitted from the LED looks brighter to human eyes.