I agree, when major things like toe pushing, hunching and staring at the ice are corrected then a lot of improvements in the basics come back to good edge and body control (and added extra knee bend!
). I think that some skaters don't have the degree of edge control that they should for their level. I know my coach feels that the UK field moves tests don't really teach edge (and body) control as well as figures did.
A while ago one of my skating friends asked me who a skater was. (She had not seen her before at our club session). The skater in question was just skating round and round in circles chatting like a lot of others but you could just tell, even with her back to us, that she was a fabulous skater. She had lovely poise, grace, knee bend and extension and a beautiful fluidity over the ice. No wonder as it was Sinead Kerr.
I watched her doing a Dutch waltz with one of our dance judges during a dance interval later on... Wow! It is not the most interesting of dances to watch normally but it was just captivating to see someone of that calibre doing a simple dance with such skill, edges and control (and that was with her really holding back so she didn't kill her partner!
)
I don't know if a dance coach would be any better at teaching good basics than any other coach. Any coach with good attention to detail could and should be helpful!
My coach is having me spend an inordinate amount of time working on improving my basics (especially getting deeper edges, better knee bend and better extension). I did some figures as a kid so when I returned to skating as an adult my edges weren't too bad (for beginner levels anyway, when I didn't need much speed). Now my ice dancing is improving a little they apparently need a whole lot of work!
Not sure the work on basics ever ends no matter what level someone attains!