Ok, here's my conclusion based on many hours of dogfight servers in Il-2 with ~40 people on the server, concentrated in one general area of the map. Icon ranges can vary from none for enemies, to black icons out to 3km for enemies (the black color makes them a little less obvious).
My first observation is that it does not make cherry-picking easier. The cherry-picker's M.O. is to target the highest bandits first. The highest bandits are most often others who are trying to cherry pick. Therefore, any gain in stealth with short icons is balanced out by the greater risk of being cherry-picked while trying to cherry-pick. Experience has taught me that longer icon ranges generally afford me greater certainty about when it is safe to cherry-pick, so I can devote more of my attention to my targets who might also be more aware of my presence. In any case, the net difficulty change of cherry-picking is somewhere close to zero.
My second observation is that it is easier to get bounced with short icons if you do not compensate with more frequent scanning of the airspace around you. If you're used to scanning once every 10 seconds, and the icon range is cut in half, you need to scan every 5 seconds to have the same degree of SA.
My third observation, and something which no one else has touched on yet, is the contribution of icon ranges to furball dynamics. Generally, longer icon ranges tend to spread out fights simply because enemies at greater ranges are readily visible. You think more carefully about jumping into a lower furball when you can see enemies 5km out. You weigh the enjoyment and utility of the close fight with the enjoyment and utility of fighting the enemies who are a little further away. When all you see are some dots in the distance, human behavior tends toward the immediate; you target the bandit you can see. Short icon ranges have the unfortunate consequence of coagulating fights, where the annoying tendency to gang-up 3 or 4 to 1 on the nearest bandit is amplified. I think we can agree that this is the last thing AH needs.
The aspects of surprise and stealth are what make limited icons enjoyable and good for scenarios/FSOs, etc. The loss of SA is ideally compensated for with good squadron communication, and a knowledge of where friendly units should or should not be operating (this is one of the reasons why teamwork is frequently the deciding factor in scenario play, and not individual skill). Greater SA allows for more commitment to a fight and the goal of shooting down an enemy aircraft. Greater SA also means a lower implied risk that comes with less airspeed and less altitude. So longer icon ranges encourage the raging low altitude furballs that AH is known for because they make SA less expensive. If icon ranges were made shorter, some fighting styles would become less successful, namely those that depend on the cheap SA that current icon ranges afford, e.g. the lawn-mowing furballer.
For my part, although I often deride main arena gameplay, I do not put any blame on icon ranges. I like that their most important effect in a chaotic arena is to keep fights spaced out, and to give a little motivation for engaging the bandit who is a little further away than the one who's already fighting a friendly right in front of you. I've tried online air combat in arena environments that have no icons at all, icons for friendlies only, icons out to 3km, and what AH offers, and I believe that for a free-for-all arena what AH offers is best.