Here is my son's take. He is a Level 8.
He says that in his experience, there are kids who will use rips (or other claimed pains) to get out of doing something they do not want to do. Maybe this is more prevalent with boys than girls, I would not know- he says it is more prevalent with younger boys by which he means 12 and under.
If a kid has a reputation for doing this, then the coach is going to be more hardnosed about it or at least may suspect the kid is overstating the pain. Think the boy who cried wolf.
If a kid has the reputation for not doing this, their claims of being in pain would be taken more seriously.
My son says he has worked with new rips and not worked with new rips. It just depends on the rip in question and how bad it hurts. He says it is the depth and not the surface size of the rip that makes it more painful (generally.)
Also at his gym, they do not work Hbar right after Pbars typically. The rotation is normally Pbar, rings and floor one day, and Hbar, vault and pommel the next. (Usually.)
For a situation like the above, the coach would have the kid tape up and give the event a try, and if after trying, the gymnast says it hurts too much to do the planned event, they would go do something else that is less likely to hurt the rip. Another event or conditioning etc.
Also my son says using straps on highbar can help make it not as painful to work hb with a rip.
Rope climbs are typically used for conditioning. They are also used for discipline when a kid is acting up. Boys at gym practice need lots of (appropriate) discipline because gym practices are long and somewhat boring and particularly for boys, that can be a real challenge. Even the most devoted boy can lose interest, goof off, and cause disruption. One way a kid might act up is not wanting to work hard on the scheduled event, and wanting to do something they find more fun or whatever. A reasonable number of rope climbs as a consequence for such relatively minor misbehavior or disrespect is appropriate in my opinion, assuming it works for that particular kid or group of boys. I would not call it abuse!
I am not clear on for what purpose the coach suggested a rope climb, obviously if was ordered with the intent to hurt the child who has a rip, that is abuse. In fact, rather sick abuse of the Doloris Umbridge variety! But is that what happened?