My dude Herc has repeatedly said that he would fight for humanity's survival. If you're suggesting the best way for him to do that is to throw the fight, give up his own honor, and die, then sure, that's your morals. But Herc is sitting here mid-fight moving the hearts of both humanity and gods with his speech about loving humans, and literally everyone on both sides loves him. If anyone can find peace between humanity and gods, it's the half-human half-god who all humans and all gods see as a personal friend.
The suggestion that he's a hypocrite because he's trying to beat Jack is ridiculous. He's not going to accomplish anything by refusing to fight for the gods, and he's not going to accomplish anything by intentionally dying.