Tommy, I think you are off base for pro's and top players...but maybe right on for average players.
Pro's average highest, against par, on par 3's. Reason is length. They can hit many or most par 5's in two. They often putt for eagle. On par 3's that never happens. They must hit a full shot, sometimes with a longer club than they hit into par 5's for their 2nd shots. Instead of putting for eagle, they putt for birdie.
Average players are spotted their drive on par 3's, and only must hit their approach. That is why par 3's are often rated as the highest handicap holes. They are the longest holes for pro's, but the shortest for average players. With par 5's, it's just the opposite. Which is why they often are among the lowest handicap holes.
Interesting. Our club changed its hole handicapping few years ago from having the 1 handicap being the toughest hole to having the 1 handicap hole being the hole in which a higher handicapper would benefit most from a stroke when playing against a lower handicapper. Thus, number 3, a 450+ yard, into the prevailing wind par 4 (the previous 1 handicap) became the 13 handicap hole, and number 5, a longish par 5, became the number 1 handicap hole. As I understand the logic, 3 is a hole in which a low handicapper is more likely to bogey than birdie, so a 12 or higher handicapper would be less likely to need a stroke. On the other hand, 5 is more of a potential birdie hole (based upon statistical analysis of scorecards over a period of time) for a lower handicapper and more likely to cause a bogey or higher for the high handicapper, so that's why it's rated more difficult (i.e., if you have a stroke, you'd get it on that hole rather than 3 because you're more likely to need it there).
We always joke about how much easier number 3 got after they revised the handicaps.