Missing out on .5 hp of damage per attack bothers me much less in game than another player telling me I should play his idea of an ultra-optimized character. I am not trying to win a tournament. I am playing a story-based game in which enjoyment is based on the story were are creating/telling. It is more about the journey than the destination. I don't need the rules to give me a reason to use my weapon of choice.
This axe was my father's axe, and his father before him. It is the weapon I know how to use best. It honors their memory. It has a long history.
If a fellow party member questions my choice, I might explain it to him. If he makes fun of my choice or tells me I am stupid for making my choice, he will end up with a fat lip. In character.
If another player tells me I am not optimized, I will say I know, but it's my character. If he says "Well that's just stupid" or "That's just wrong" I will know one of us is sitting at the wrong table.
All true for you.
For me, my character does not know how to use the axe best unless I have a feat or ability that makes me use it best, like weapon focus or specialization in 3rd. My character will quickly learn that his father's axe doesn't hurt many of the evil creatures I fight, so I need to pick up and use a magical weapon. If I have any control over what type of weapon that might be it might as well be the most damaging weapon I can get why wouldn't I.
The game needs to back up the story, I wish damage was based on class and less on weapon choice that way it wouldn't matter if your character uses his fathers axe, mine uses a great sword, or the halfling uses a frying pan.