Cropping image breaks the origin and other points in the sprite, which is quite important for most gamedevs.
I also recommend you to use Spriter for animations for a better and faster workflow in dealing with sprites and animations.
No it's not.
Like UberLou said. I keep all sprites animation frames raw and only crop them when I'm sure I won't modify them again.
So why won't C2 crop them when exporting? Is there some logical reason for this?
Because collision polygons are depending on and limited by frame size (which is stupid by design). You can't make collision polygon bigger than frame.