"Is it for quicker spool up time or actually to decrease stress on the brakes on the ground?"
It's not so much a case of "high and low", but "high and normal". High is for approach so that spool up time is less for go-around... and, for many aircraft, when bleed air demand is greater than normal (such as when anti-icing is required).
Low/minimum/normal (or whatever you like to call it) is for economical flight/taxy. I'd be more inclined to think that better braking is just a non-intentional side effect.
The time delay from touchdown to normal idle varies depending on the aircraft type.
Rgds.
Q.