It did work out that way in my own life.

There's a Dilbert cartoon in which Dilbert thinks he's really just been faking it since sixth grade.

At age 17 I went through a bit of hell bad enough that I don't particularly want to talk about it, and three weeks later woke up one morning and realized that I would never feel like that Dilbert cartoon again. Literally, just woke up in the morning. It wasn't the result of any epiphany, it seemed more like something biological my brain just did in response. My main reaction was, "Why couldn't my brain have done this three weeks earlier when it would've #$&%ing helped?"

Not sure how that squares with the research, and I couldn't point to anywhere in my life where it happened except that one point.

However, the actual literary logic is something more like, "Once you show Harry thinking his way out of Azkaban, it is no longer possible for him to lose an even battle to Draco - the reader won't believe it." I don't think the 'power up through trial' thing is actually unrealistic, I mean, if I come out of this planet alive I'm probably not going to be fazed by much after that. But it's the more fundamental literary reason why so many stories work that way. You will perceive that this also points in the direction of, "Being run over by a truck isn't the same as punching the truck to a standstill" in terms of whether you powered up after that.

Even so, imagine Methods!Granger fleeing to the bathroom after just hearing Ron call her a nightmare. That could've happened in Ch. 9, maybe, but now Granger has fought three older bullies successfully and you'd be, like, "Yeah right." But she hasn't been to Azkaban, either.