Wouldn't you want to have as much evidence as possible if that was going on??
I was thinking about it from the coach's end - there are a lot of opportunistic lawyers out there who manufacture false claims. And a lot of potential jury members who don't realize just how much communication is necessary for an elite level athlete. Plus, any ordinary person, including jury members, is going to be inclined to believe a child who claims abuse over an adult who is accused of abuse. I assume that most of the time that inclination is correct - but almost any coach deals with a lot of students, so some care is needed. That's a substantial part of what "Safesport" is all about - insuring that you as a coach are provably innocent, because you only interact with the student in the presence of other background-checked adults. Something you can't do in this type of communication.
I was on the jury in a civil trial where the plaintiff's lawyer kept very obviously manufacturing evidence - including deliberately misquoting what the defending party had said in court right in front of us. Pretty much the whole jury ended up believing the accusing lawyer. Both parties were obviously lying about some things. I wound up concluding that most U.S. civil court trials are decided wrong, because the honest party probably doesn't manufacture evidence, and because plaintiff's lawyers usually have the opportunity to make more money, because they often work on a percentage of the take. (In U.S. civil trials, as the plaintiff's lawyer explained it, cases are supposed to be decided on the basis of a "preponderance of evidence", using "the 51% rule", which I guess means that the side that manufactures fake evidence will generally win. I wonder if the same thing is true in countries like Britain, where there are trained professional jurors...)
And a lot of elite skaters and their parents who get very upset when their kid doesn't turn out to be Olympic material. Apparently, it isn't actually possible to figure out years in advance, who is going to reach the very highest levels (e.g., Davis and White weren't favored to reach close to the top until shortly before they made it to the Olympics, and the same is true of a number of other Olympic skaters) - so a lot of elite coaches honestly tell some of their students they have the potential to be the best in the world. The students and their parents put in a tremendous amount of time and money into the sport, and the students do a lot of damage to their bodies pushing them to their limits, but most of those kids don't make it to the top, for one reason or another.
Sure, from the skating parent's end, evidence is a good thing. But a "smart" abusive coach would avoid leaving traceable evidence. OTOH, from what I understand, if a conscientious non-abusive elite level coach is doing his or her job, they often communicate with their elite level students a few times a day, giving encouragement, helping through various problems, etc. (For starters, they are probably giving at least one lesson with that student most days.) Just like a serious mentor in other fields - e.g., a thesis adviser might do that too. But leaving evidence of this, and providing too easy an opportunity for extra communications, leaves a situation an unscrupulous lawyer can take advantage.
Maybe none of this applies to non-elite level coaches. But who else would need such frequent communications as an app would produce? Many of the lower end coaches I know feel a need to limit the amount of unpaid communication with parents, who can be very demanding of a coach's time. I suspect most coaches of lower level athletes in other sports feel some need to limit the amount of unpaid interaction time too.
In terms of detecting abuse, I think that from the parent's end, talking to the kid and watching their interaction with the coach(es) makes the most sense. But I've never been a parent, and maybe don't understand how difficult abuse is to detect.