I don't want this to be a flame war or argument as I am not an expert and know little about crocodiles. However, I think your info on alligators is not entirely correct. Google "swamp pole gun" and one should find the most common caliber to kill an alligator is a .22LR. This is in order minimize damage to the hide.

A shoulder strap pocket can be accessible and concealed. Just leave the zipper partially undone.

I agree that for most people the utility is more psychological than anything else.