Here is the average non-coincidental penalty differential (penalties drawn minus penalties taken) per 82 games and 15 minutes of icetime for each position:
I think you can construct some pretty compelling arguments for why centers show so little variation in their numbers across all man-advantages. But why do right-wingers have much better numbers than left-wingers? Simple answer: Dustin Brown. He is far and away the best in the NHL at drawing penalties, and he drives the numbers to a different result:
Almost half of the difference between LWs and RWs is Brown's skill. Lest you think drawing penalties is not a skill for forwards, here's the year-to-year regression to the mean and R^2 for forwards with 500+ minutes at 5-on-5:
Taking penalties has a non-skill component to it - that is, some coaches will send players out to intentionally take penalties. Opportunities to do so will vary from season-to-season, and by whether Daniel Carcillo is seen as an agitating physical leader or an undisciplined goon.