eteri should listen to her skaters? What are you talking about here? Her skaters do what she tells them not the other way around
In principle a student/skater will listen to the coach within reason.
Let's look at this rationally.
Someone is spreading a rumour that it is a serious injury, but what is a serious injury? And can that rumour be trusted? I don't someone can jump quads so easily in a warm up with a
serious injury. Or is just some kind of excuse coming from Margo's camp to excuse such a bad loss to her rivals, potentially not being in the senior team.
I don't really believe someone with a serious injury could skate a short program so brilliantly, jump flawlessly in the warm up, then suddenly fall apart in the free skate itself. This would indicate a psychological failure, rather than a physical failure.
Sure, could there be an injury. Of course. I would be surprised if any skater 6 months into the season isn't carrying an injury of some kind. This is the nature of sport you are balancing up whether to take the risk or not. This is the Russian championships, it is the biggest event of the year, she wants to retain her title, she wants to be on the national team, there is many months of rest after this event if needed to recover, they made a calculated decision that the juice was worth the squeeze. Is this right? I don't know it's a personal decision. It's not a sport for risk averse people.
If we only allow skaters that are 100% healthy to skate there won't be too many competing. I don't think Malinin would have taken part in the GP final, I think Glenn was carrying an injury as well. They made the calculated decision to skate and it worked out well for them.
It could be a situation like with Usachova where Daria and her mother were demanding they go onto the ice while Eteri was against it. I'm sure it's not Eteri having the final word, it's the skater and the parents making the ultimate decision. Valieva came back from some fracture in her leg with just three weeks of training at the JGP final in 2019 and skated without ultra-c content. So they do scale it back when necessary.
We don't know the nature of the injury either. If it is some kind of stress fracture (which is simply a part of the game nothing to do with Eteri), then she probably skated after a doctor said it is likely no more damage will be done to it and knowing that there are many months of rest ahead if needed. If it was early in the season, she might have sat out to prepare herself for the big competition.
If it was some kind of muscle strain, again this is something that can be managed after the competition.
Yes, in a perfect world everyone waits until they are completely healed until they skate, but ultimately athletes carry injury and make calculated gambles with their health in every sport. The flip side is if athletes aren't allowed to perform carrying injuries, then they will simply hide injuries from coaches, support staff, parents in order to compete.