And while the rule encourages better rotation, it leads to messier programs by indirectly encouraging falls, two-footing, turnouts, etc.
This is the only part of your post I have to disagree with. I don't think that the double penalty for underrotation indirectly encourages falls, two-footing, turnouts, etc.
It's not as though skaters can choose "Oh, I better not underrotate my jump because of the harsh penalty, so I will fall, two-foot, or turn out instead."
In many cases they do those things *because* the jump was underrotated. Which is why I think there needs to be a better way to punish a jump that is two-footed because of underrotation more harshly than one that's just underrotated; as it stands now the only difference is likely to be -2 vs. -3, or -1 vs. -2 in combos.
At least with jumps that result in falls because of underrotation there is also the fall deduction in addition to the downgrade and -3 GOE.
I haven't done a statistical analysis, but I would suspect that the percentage of jumps with falls that are downgraded is a lot higher than the percentage of jumps without falls that are downgraded. Incomplete rotation is a very common reason for falling.
I would also expect that the percentage of two-footed jumps that are downgraded is higher than the percentage of jumps landed on one foot that are downgraded. Underrotation is also a common reason for landing on two feet.
What I think the double penalty does encourage is for skaters to play it safe in terms of their jump content. There's not much incentive to attempt a triple axel or quad if it's going to be downgraded and you would get more points for just doing a good double axel or triple. Same for triple-triple combinations in which the second jump is likely to be downgraded.
Under the old system, although cheated jumps were not given full credit, there was some reward, or at least skaters believed that there was, for attempting the more difficult jumps. A cheated triple was supposed to be considered worth less than a good double, but there was still a sense that it was worth more than a bad double. Now it's officially worth the same as a bad double.
So you got a lot of skaters attempting jumps that they couldn't really rotate yet in order to establish themselves in the judges' minds as skaters who were attempting the top jump content.
Under the current system, they would be giving away points by attempting jumps that they haven't mastered yet, so in many cases they make the choice instead to stick to the easier jumps that they have already mastered and that they can enhance for higher GOEs. This is especially true at the lower levels, but we see it at elite levels as well.
There are still some reasons why skaters would include jumps in their programs that they haven't mastered yet. If they can rotate the jump at least sometimes in practice, then putting it in the program helps them get experience doing the jump in competition, which can help them psychologically to become more consistent with it as they master the technique. And there may be at least a slim chance that they will actually rotate it enough to get full credit . . . with more experience, that chance may become larger.
That motivation becomes a tradeoff -- is it better to do an easier jump that can earn +GOE and get more points at this competition, or is it better to do the harder jump that will sacrifice points today but store up competition experience with the jump that may pay off next year?
Also, at the elite levels, because of the set number of jump passes and jump repetitions allowed, attempting a quad or triple axel that is likely to be downgraded can still provide more points than whatever double jump could have filled that slot after all the triples the skater has mastered have been used up.
In practice, the only triple with three air turns is the 3A. As it currently stands, a triple has at least three turns, not all of which must be in the air. That standard has probably been that way ever since the first triple was ratified. You'd know better than I. Otherwise, we could call the rest of the triples as doubles, the doubles as singles, and singles as hops.
