I'm taking a step back here and focusing on a larger scope for second...
The thing that makes a coping strategy unhealthy is that it doesn't work - it doesn't address the actual problem.
This is the core of our disagreement here, and why I think so many writers fail to grasp the Bat-family. The Bat-family is one giant coping mechanism. Batman exists because he can't say he misses his parents and move on past being an eight year old in an alley. Oracle exists because Barbara can't accept she lost control one night and her entire life is looking through every peep hole for danger. Batgirl using combat as a way to express herself is a coping mechanism because she can't put how she feels into words. That's what makes them work, that's why they're the best at what they do, and that's why writers stupidly keep trying to fix them and make them happy people.
Batgirl's coping mechanism fails in later issues, not because coping mechanisms within the Bat-family are bad things, but because coping mechanisms in the real world are bad things, and 99.9% of writers who write these books insist on cramming real world psychology into the lives of billionaire vigilante fighting savant super hackers.