I find having icons on necessary if I'm to have a decent chance of spotting other aircraft (whether friend or foe), but I think it would be a neat feature if the icons disappeared again once you got in close, maybe inside 800-1000 mtrs. Thus, in say a dogfight you would have to recognise aircraft type to establish whether it's a friendly or a bandit, estimate range to the target in the gunsight, etc.
I have, of cause, no idea whether this would be possible to code in the game.