Nthuz,
ITA. Great analysis. Although skaters need external hip rotation for spread eagles, they pretty much need 180-degree turn-out and they basically either have it or they don't. But I agree that's not for a ballet teacher to instruct a skater in. It's the place of the skating coach because the way a skater achieves the turn-out for a spread eagle is different than the way a dancer uses turn out. Skaters work mostly with the hips in parallel and as you said, with hip flexion (bent forward for stroking). Too often ballet teachers think ballet is the be-all end-all technique for any athlete and they try to turn the skater (or whatever athlete) into a ballet dancer, which is wrong. What ballet can do best is just what you said, develop core strength and I would add awareness of body movement, how to stretch out and become exapansive as a skater.
One thing I do think is that ballet can help skaters learn to move their arms from deep in the back, which also strengthens the core integrity, IMO. You're right that the choreographer or coach sets the arms, but a good ballet teacher can train a skater how to initiate arm movements from the spine and to connect the spine to the center.
But to try to make skaters into ballet dancers, no. You're so right; it does more harm than good.
Rgirl