Hanzou
Grandmaster
I am sure there is something to what you say above. But I don't see an answer in there about differing rule sets. You are describing different reasons for studying one of three martial arts, not how different rules sets might place one at a disadvantage against another. Or don't you think competition rules of different arts give them advantages over arts that don't learn competition within those rules?
Boxing's rule set is only limiting if the boxer gets taken down. On its feet, boxers can hang with anyone. Wrestlers rule set is only limiting if they encounter excellent striking, or they're dealing with submission grappling. Both of their rulesets come from competitive sports.
People are finding it difficult to see exactly where Aikido is effective. Since it isn't a competitive sport, it really shouldn't have a rule set that limits what it can do, but it does.