The other thing is that the story puts a thumb on the scales, but doesn't hard counter blind stupidity. We're reminded time and again that great named people have been brought down by attempting to fight entire armies. Sure, they are ludicrously favored in each individual matchup, but roll enough dice, and the universe eventually misses one.

This is basically how Cat got him shot. The rest of the arrows did miss, after all. If he'd played smart, his hero-shield would have definitely let him survive that, but the combination of arrogance and a loooot of arrows meant one leaked through.

Now, in fairness, Cat definitely does have some protagonist edge. She gets lucky sometimes. However, it's not so easy or painless as to reach Mary Sue levels. The situations she gets herself in still feel like legitimate challenges. Mostly. Under winter, she got pretty crazy, but that's mostly past now.