I think the character is pretty cool, and his accomplishments and attributes are impressive, ESPECIALLY considering that he was doing all this stuff with only a bow and arrows. My point is not that I can't see the agent for the bow and arrows, it is all about how much MORE impressive that agent would be with a frigging GUN. Why carry the bow, when it can't do anything that a gun could also do, more easily and efficiently. Maybe he wouldn't let a (selectively)skinny chick beat him in a hand-to-hand fight, if he had a spare arm to fend her off with, instead of needing both of them to shoot. Maybe he could put those extraordinary reflexes and aim to use with a gun in each hand, to kill two foes at once, rather than use both arms to kill one guy at a time.

Think how much more effective he would be if he had dedicated all those hours he spent on archery. Since this is a WoT fan community, you should recall the various times in the series where Jordan points out the long period of time required to learn archery, and why point-and-shoot weapons like crossbows [or guns] are preferable if they can increase their rates of fire. Mat Cauthon and co would be facepalming at the idea of a man using arrows when he has access to tiny little dragons that can shoot faster than a man can count.

If they have guns that can shoot the fire of an ass-cheek-norsegod-robot, they could rig up a multipurpose gun that could do all the things his trick quiver could do, WITHOUT being a huge thing he has to carry that hurts when he lands on his back.

And the heroism is undercut if the threat is mild enough to allow Hawkeye the luxury of using a second-class weapon. The point is they are supposed to be going all out and pulling out all the stops, hence the justification for loosing the rage beast. Yet, there's Hawkeye, farting around with a less effective weapon, because it looks more badass. This is not Ankh-Morpork they are defending, where the chances of shooting down a monstrous flying threat to the city actually improve with all the handicaps you pile on your marksman!