Both reasons are correct I believe. High idle is required to improve spool up times in flight. However, on landing, as you say, low idle reduces braking activity.
Two points:
1. There is a 4 second delay after toucdown before low idle to improve reverse spool up time.
2. High idle is a pain in the descent as it makes the 737 very difficult to 'go down and slow down.' High idle is 32% N1, and for comparisson, you only need 55% on final approach with flap 30, and 50% with flap 15!
Low idle is 22% N1.