We do it because it shows a duel history. Some of us are warriors, and like to compete with eachother. Even if they have no meaning to you, they mean a lot to us.
I'm more inclined to believe that they are not so much duelling history, but numbers. Numbers that can be increased. And we all know how much appeal increasable numbers have on players.
The DP measure how much you have duelled, sure. They even measure what the approximate relation, as percieved by the system (probably by merely comparing the amount of PP each char ever gained), of the duellers was. Great. But I don't see your chars compete against eachother, I see you players compete against each other. DP are PS's idea of "lvl" in "Wutz Ur lvl?".
If your characters are warriors, then why do they bother calculating some abstract number, thereby obliterating any and all individual cases of fight? Wouldn't they be more likely to brag about how they managed to defeat X, even though X had been defeating Y with ease just days before? Wouldn't the respect gained from the canny and memorable fight make the word spread? Wouldn't they rank only by tournaments, not by training fights?
I guess no, because within the fighting system, there cannot be any canny and memorable fight, not even with hit&run. I guess that there's so unrealistically much fighting going on that no single fight gets remembered at all. In fact, there are so many fights that the individual fighters become insignificant, and the only thing that remains is some statistic. A statistic that ultimately doesn't refer to a character, but to a player, as was the purpose all along.