There's many reasons for bowhunting. One of the most common is the closer range one is required to get to the prey. This takes much more work than picking an animal off from 250-ish yards with a precision rifle (provided the rifle would take tremendous skill at that point, however hunting is about the track as much as it is bringing home the meat...or unfortunately, trophy as some would have it). Also in the US, a person who's not allowed to touch firearms for legal reasons can often have access to bows.

I hunt, but follow the "eat what you kill" rule. Currently, I'm a shotgun hunter, but am moving towards handguns, as they're easier to carry about. A 8" or longer barrel pistol of quality make can provide plenty of accuracy up to 100 yards, which is fine for most game.

One thing that hunter did wrong was not stand hunting. If he had determined common traffic areas and set up a stand downwind, he could get an arrow off from relative safety. Instead he made two mistakes, he revealed himself to the Bull Moose, then proceeded to shoot at it without cover. Just more "reality TV" idiocy IMO.