In all fairness - Some coaches who are high class athletes can teach very well, even to people like me who aren't anything like that.
E.g., I took kayak lessons from a world class competitive kayaker, possibly the best teacher I have had in any subject. He was very disciplined, superbly organized, and very good at analyzing what a student was doing wrong.
OTOH, I've gotten great tips from non-coach skaters who were just a little better than me at something, and were struggling with the same things. Some of the best tips have been at skatingforums.com, from people who have never seen me skate.
I haven't had all that much luck with any of the books and videos on skating I have tried to read or watch - they are poorly organized, and/or they explain the gross motions without talking about the detailed little things that make the bigger things possible. That's a problem for me - I tend to learn best from books, and my approach is very analytical. The best teacher so far for me was someone who understood the analytical approach.
And some things I may never get. E.g., good, well controlled spins, or well controlled rotational jumps.
I've got (ice dance) progressives down pretty well. That's because one of my first instructors (who was an extremely good skater) drilled me on it in a very disciplined way, lesson after lesson. He had a set of standardized drills (similar to Annie's Edges, I think) that he made his students practice forever and ever. He emphasized the basics - posture ("sit"), very deeply bent knees while I was over them, deep edges, and going so low that each leg fully extended straight on the ice at the end of pushing outwards. But I often couldn't understand him (or him, me - he barely spoke English) on many more complicated issues, which was extremely frustrating. He did much better with students who already knew the basics - including elite skaters, and most of the coaches I tried after him.
Incidentally, the idea you mentioned, of learning each skill progressively, building each skill on prior skill's foundation, in an order that makes it easiest to master, is something that PSIA - a ski instruction organization - has down to a tee. I don't know of anything or anyone comparable to that in the skating field. You might love taking ski lessons from a good PSIA instructor. Now that I think of it, those were also important elements of the teaching style of the great kayak instructor I mentioned.
I guess I do best with a strongly disciplined and organized coach, with strong analytic skills, and lots of repetition, including a sequence of drills he/she keeps coming back to, and I can keep working on. (But that is specific to me, not you.)
Many coaches can adapt somewhat. If you understand what teaching style you need, it is extremely important to communicate that to the coach, from the start.
(Also, unlike that first ice dance coach for me, you should pick someone of the opposite gender, so you can dance with them.)