Particularly in crucible, where one of the challenges is often to use a specific damage type but you don't really have time to switch weapons during the match. I often feel like I make no progress in my first match of the day because I have the wrong weapons equipped.
It would also save time on challenges like "loot a lost sector in _____," because we could go straight there when we head in from wherever we were before, or challenges to kill a specific enemy.
This seems like a pretty small change, but over the course of a day it would save a bunch of time for almost every player.