What's the advantage of turning on "brake on stop" on BLHeli_S?

Brake on stop does exactly what it says: when you cut throttle to 0, break actively by connecting all phases to ground.

It enables the propeller to stop right away when throttle is down and not armed. So rather than the props spinning down at their own rate, the props will be forced to stop.

Brake on stop is a fixed wing feature because on a wing a spinning prop can cause drag if you wanted to glide around.

Brake on stop is not the same as damped light BTW. Damped light is on all the time on BLHeli_S escs.

I was hesitant at first, but i've grown to like it on my quads. Props are a bit more safe when landing on rough terrain.

Not sure wether it consumes a bit of power though?

I personally like this feature especially because is a propeller saver !
there were few times I was losing the control of the quad and then I shutdown motors to avoid breaking props and burning escs & motors, and since I started to use it, It changed it, never cautch fire again