If the chest is just too much trouble (which is of course completely arbitrary and can be different on any given day) I'll leave it, but I'd say the vast majority of my shrines are fully cleared.
I killed two Hinox today via the awe inspiring method of standing on a ledge over them and raining down bombs and bomb arrows until dead. I am a stud. If for whatever reason you need Hinox parts, though, it's not a bad idea to mark a location or two to return to after they respawn.
A minor control complaint (spoilers for side quest):
I think you know a game is good when grinding for supplies doesn't really feel like a chore. I'll just be jogging along to my destination then I see that sparkle of something collectible and the next thing you know it's two hours later and I forgot where I was going in the first place. Also one of the reasons I almost never horse - I'm having too much fun running around, climbing all the trees and scaling all the cliffs.
Finally I feel like a real moron, but I just found the inventory sorting button today.