Is there any reason why there could not be different rules for men’s skating than for women’s? In gymnastics, for instance, women do not do the high bar or rings. These strength apparatuses are just more appropriate to men’s gymnastics than to women’s.
In Gymnastics, women uniquely do the balance beam, uneven bars, and the thing on the floor with the ribbons/hula hoops...men uniquely do the pommel horse, parallel bars, and rings (maybe something else I'm forgetting). In Figure Skating, men generally do more technically difficult jumps and steps, where women uniquely get points under the ISJ for doing a spiral. I think these activities are indeed "more appropriate" for men and women to compete in.
1. Raise the base value for triple Axels.
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But then, in order to preserve the idea of a “balanced program,” we would have to raise the values of spins and footwork, and also give more weight to program components. Competitively, nothing would change except that everyone would get a few extra points across the board.
No, there is a very basic but significant change you are proposing. This is the equivalent of keeping the current point system for the 3Axel and the spirals, steps, PCS, etc. intact, but making every other jump's base value worth ~0.5 points less. Is there any particular reason why you want to downgrade the relative worth of all the jumps (except the 3A)?
2. Combine the flip and the Lutz into a new jump called the “left foot take-off toe-pick assisted” jump.
The LFTOTPA (or RFTOTPA for clockwise jumpers

) could go off either the inside edge or the outside edge, skater’s preference. A clear, deep outside edge is a feature for +1 GOE.
Pro: This would eliminate all these judgment calls about “e” and “!” and whether judges must follow the tech specialist's call or score by their own real-time eyes, etc. It would also prevent (via the Zayak rules) skaters from omitting the edge jumps (loop and Salchow).
Con: This is a cop-out. If you can’t do a proper Lutz and a proper flip, go home and work on them until you can.
It sounds kinda crappy (explained below), but it's not a horrendous idea. Sure, as you said, they already did it for the 3ToeLoop. However, sometimes the way people do 3Loops and 3Salchows look similar to me, too. So if we're going to do that, might as well apply the same principle to the 3Loop/Salchow.
Now most women's programs will have:
3Toe (your pick of ToeLoop or Walley)
3SalLoop (your pick of Salchow or Loop, Loop +1 GoE)
3Flutz (your pick of Flip or Lutz, Lutz +1 GoE)
2A
Cool...3 different types of triples. Sounds like a backwards step to me.
I think it's "crappy" because if we want skaters to train demonstrate different skills (in this case, edge control in jumping), we should maintain the difference between a 3F and a 3Lz. I've heard half the reason the flutzing and the lipping became so common is because judges started to not be so picky about identifying and penalizing this type of cheating.
A better option mentioned elsewhere in this thread is something like a +5 point bonus for doing five different triple jumps--that's pretty nice, it's like getting credit for doing an extra imagined triple jump.
That, on its own, would also add further incentive to possibly doing a 3Axel without needing to raise its base value--a girl could substitute it for any other triple jump she may have trouble with (e.g. 3Lz), and in the process, she is doing a jump that is worth more. I do not think a higher base value at this time is merited or justified. You never see a 2.2 difference of base value for any other half-rotation's difference. 2Lz to 2A is 1.6 difference. 3A to 4T is 1.6 difference. The difference between a hypothetical 4Lz and a 4A is 1.5 LOL!
In general, I don't like the idea of different base values between men and women. A couple reasons include consistency/simplicity of the judging system; and also for the implication that women are physically inferior in terms of athleticism. I realize that the reality does point in that direction, but if a woman can do a 3Axel, she should be given credit for it along the same lines as a male's 3Axel, no "female bonus".
I don't even like the principle of different PCS factors between the men and women (1.0 vs. 0.8 in the SP, 2.0 vs.1.6 for the LP) because although I understand the reasoning behind it, I think it would have been better to make it factored against the actual TES a skater gets. Something like (TES x 0.5) + (raw PCS x 0.5) = Total Score. That way, the factoring correlates automatically to the TES instead of the fixed/absolute/embedded factoring.
I think GoE's also need to be factored to the element they are referring to...but related to this topic are the standards to which they are applied. e.g. "good height & speed" for a woman doing a jump may be different for "good height & speed" for a man. Should we make it absolute, or relative to the respective sexes?