You’re overgeneralizing things. “Healing magic” is a laymare term that refers to Partial Acceleration and the more recent Mending.

Partial Acceleration is the oldest form of time manipulation magic. It predates antiquity; literally was produced before recorded history. It’s advanced, but one of the most finely tuned branches of any defined school of magic. Using it properly is sort of complicated and requires a lot of preparation before, during, and possibly even weeks after the procedure. But if done properly, there’s no real danger in advancing time on a specific part of your body; the rest of your body will compensate.

However, it will only heal what the body is naturally capable of healing on it’s own. I don’t know what happened to the pegasus that sent that message. If s/he crashed through thick glass and completely mutated their wings, no amount of acceleration is going to heal what the body is incapable of healing by itself.

Mending, on the other hoof, is new. And by new, I mean like a decade old. The ponies that originally presented it as a legitimate branch of manipulation are still alive and continuing research in the field today. It’s incredibly complicated and is technically a form of forced bodily mutation. It’s thus far proved unreliable and long term effects are unknown, but in life-or-death situations mending has done some remarkable things. But last I looked into it there was a possible correlation with producing cancer in the years after the procedure.

All the procedures I’ve had that involved magic were all partial acceleration. And they still left scars.