If a skater added weight bands to there wrists, would this increase their spin speed if they could draw their hands in at the same speed as without the weights? If it worked. Would it violate any current rules of the figure skating sport? The skater would of course train to be able to keep the same retraction speed. It might negate some air time though.
Ignoring rules and speaking to physics.
To accelerate by retracting their arms they have to start at some spin rate with their arms out. Spinning up to that rate takes energy and strength from their body. If they added wrist weights and nothing else changed, they’d be unable to spin up to the same starting RPM using the same techniques they do now.
So first we have to decide what the limiting factor is on them spinning up with no weights. Strength, control, time between maneuvers, or ???
I don’t think that their initial spin rate is limited by energy. And in fact, when we do demonstrations of the same principle in a physics classroom, we usually do hold weights in our hands. Physically, I would expect that it would work just fine.
Rules of the sport, I know nothing.
If you have one arm out behind you, the other out in front of you, as you tend to do when skating, running, then forcefully change their positions to opposite, it will induce rotation. Now they are extended fore and aft and rotation has been initiated with the additional weight being acted against to induce it. Now you also pull the arms in close to the body. Again with additional weight. Intuitively this seems to add up to faster rotation. Of course, intuition is not physics. Often they disagree.
I watched a couple slow motion videos of jump spins. I don’t think they were Olympians. Varied technique. But basically the same. They didn’t seem to take full advantage of the physics. But that may just not be reasonable for the physical aspects.
Apparently the advantages are negated by the disadvantages.
“While theoretical evidence supports the use of weighted gloves in figure skating jumps, compensations negated their effectiveness in jumps the skaters could already perform well. Optimal implementation may be when skaters are learning new jumps.”
Up in the air: the efficacy of weighted gloves in figure skating jumps