@FSWer I'm not a coach but I can try to explain it from a skater's perspective.
When you see ice dancers on TV, those skaters have done their programs many, many times already, and done a lot of work with their coaches on those programs. So hopefully those skaters would have been asked about touching
before they started working on those programs, long before you are seeing them. That is why you wouldn't see them asking while they are on TV.
Skaters know that the man and the woman holding each other is part of ice dancing. So a skater who is uncomfortable with being touched by a partner in any way probably won't become an ice dancer at all.
Coaches and skaters have to trust each other. But coaches often have to touch their students to show them how or where to move. So if a coach wants to touch a skater as part of teaching them, a good coach will ask the skater before touching them, or before asking the skater's partner to touch them. This is particularly true when the touching involves a private or sensitive body part, like a woman's chest.
But sometimes coaches will touch skaters without asking them. Sometimes the coach forgets to ask because they are so busy concentrating on what they are working on with the skater. And sometimes, unfortunately, the coach is more interested in touching the skater than they are in anything else.
And sometimes a skater doesn't feel that they can say "no" to their coaches or to their partner, even if the skater feels uncomfortable about being touched. The skater might think that the coach will not want to teach them any more if they say "no". Or they might be worried that their partner will be mad if they say "no". So even if the touching is wrong, the skater might feel they have no choice but to let it happen. That is really awful, but it happens - and that is why asking before touching, and making sure everyone is really OK with the touching, is so important.