But you are talkiing about a progression of skills - which is different from doing each skill "right".
Examples:
1. March and glide. Most students initially think the feet should stay parallel. It's so much easier and more efficient, if you point the toes outward, and it simplifies the transition to swizzles and stroking. In fact, to emphasize this, they should be shown that if the feet stay completely parallel, no forward or backwards motion occurs. Instead what many of them misunderstand to do is to walk on their toes. Slow the nominal progress down a little, and do it right, and they will be able to skate better in the end.
2. People are often initially taught to do swizzles by pushing outwards and pulling inwards very hard. To do so, they tighten their muscles to the point their own muscles fight the motion - and become the reason they need to push and pull hard. They may be told that bending your knees helps, but what I think is the "right" way is to drop into a somewhat bent knee position, then tighten your muscles to slow it down and let the momentum effortlessly be transferred through the inside edges to pushing the feet apart. Likewise, you can straighten your knees, and as you finish straightening, as you slow down, the momentum will effortlessly be transferred to pulling the feet back together. Extremely little strength is required, and you can be almost completely relaxed. Sure it takes longer to coordinate these motions and tensions, but in the end, understanding how the body can efficiently use tensions, momentum transfer, and edging, will ultimately make everything better. Slow it down and learn to do it right.
3. People are often taught to do stroking merely by planting the rear foot across the motion, and pushing back. They should be gaught that pushing outwards SIDEWAYS is more efficient, and will ultimately allow greater speed. Granted they may not be able to do so completely at first - but they should be taught it helps, and that that is the ultimate idea. Of course, in Ice Dance, pushing diagonally back IS part of the desired form, though even there, pushing outwards is efficient - but if you watch good freestyle skaters, that mostly isn't what they do. Partly because at higher levels they are expected to come back up to speed after the most recent trick in a single stroke, which a backwards push can't really do. An ISO video makese it clear that pushing back should mostly be avoided in freestyle skating - maybe partly a matter of aesthetics.
4. People are often initially taught to initiate turns (as a simple case, to move back and forth across a line from LFO edge to RFO edge and back) by swinging their arms forward and back (and maybe to add a partial swing-roll at the end). At a later stage they are be taught that swinging the arms that is bad form by figure skating standards - that you should instead press or pull against edges, and/or twist against your shoulders. Not only that, swinging the arms that way isn't a very efficient way to turn.
5. An even better example is forward 3-turns. Same comments as above, but some instructors try to teach it only by rocking forward to the toe pick and back again. First of all, the rock back may take a fair amount of strength to do, because you are fighting centrifugal force (or maybe that is because I do it wrong?). But, also, later students are taught (if my training was typical) that letting the toe pick touch during a turn, or maybe even during a spin, is bad form in figure skating, as well as reducing its speed. A much more effective way to initiate a 3-turn is to turn the foot slightly outwards or inwards, and let the force of the ice complete the turn - perhaps augmented by twists against the shoulders (or is that an ice dance specific form?) and/or pushing/pulling against the edge. (If one of the ISO videos is typical, the freestyle standard is to do it all or almost all by pushing and pulling against the edge. I admit that often can't be taught at first, because it does involve an element of strength. But one could teach exerting some force against the edge at an early stage, and make it clear that is the final goal.)
6. It's hard for me to talk about spins, because I admit I am unable to center them - I think it has something to do with slow or uncoordinated reflexes. (E.g., if I stand on a half-bosu-ball, and bend and straighten my knees, I shake side to side. At first I thought it was strength - but it is true regardless of whether I am on 1 foot or 2.)
But, AFAICT, scratch spins are typically taught by straight demo. I will use a CCW spin as an example. The instructor starts in a pose in which the rear (left) foot points forwards, and the front (right) foot, extended forwards, points inwards across that line. They then appear (to the student's eye) to pull inwards (and if they try to imitate that, they need to pull very hard inwards) to generate the spin - much like the above dubiously taught swizzle. If instead they are taught to make the whole move a modified properly done swizzle (as per above), but in which outwards (right) foot gradually turns inwards as you bring the feet back together, there is virtually no effort required. Or they could turn the inwards (left) foot MORE to the left, to imitate the motion it will need to start the more-or-less 3 turn a single foot typically uses to start a single foot spin.
That said, since my spins are awful, it is possible I don't understand how to do it right, and this example should be dropped.
7. If what I have seen is typical, and to me the most important example of people being taught quickly to do things badly, is that most LTS students are allowed to get away with faking outside edges in initial lessons - there is little or no lean, and they may even be on the inside edge or flats most of the time. Then at a slightly later level they are expected to do crossovers - which are virtually impossible if you can't stay on a good outside edge. (I admit good hockey players do crossovers on inside edges a lot, when they are fighting getting knocked over - but I'm sure that takes a lot of practice, and it mostly isn't good figure skating form.) In fact, based on the LTS program I was involved with, that is where almost all the students drop out - partly because they inevitably fail that level the first few times, because they don't have an outside edge. The "right" approach in my view, is to spend more time balancing and mastering outside edges, until one can easily move the free foot to any position in the air, or even to practice moving it across to what will ultimately become the crossed position and lightly tapping the ice. Perhaps outside edges should be an entire skating class level onto themselves. Part of the problem is that they THINK they are on an outside edge when they are not, because they have been allowed to pass that skill, so they think they have mastered it.