I really doubt the majority of people who do not engage in a fight do so because of their rank. I think it has a lot more to do with confidence, plane match-up, E status, fuel remaining, ammo remaining and a host of other factors.
I would bet that if rank were taken away you would see little to no difference in the arenas other than the loss of some of those who do like to play for score/rank. It is, afterall, a game, and most games have some type of scoring system.
I'm just curious why you're so worried that someone ran from you anyway? I count those as unrecorded wins.