Well at the very least Barbara must believe that due process and civil liberties are at best ineffectual, if not counter-productive since she violates both as a matter of course. The idea that an otherwise intelligent person would do these things solely because a personal role model does so seems like a bit of a fallacy, no? Indeed, it rather paints her as a zealot at best, or a moron at worst.
That's applying real-world logic to a comic-book world, which is the fundamental failing of all the "Batman is crazy/neurotic" theories. In a world where Superman, Wonder Woman, the Flash, etc. exist, it's not abnormal for someone to choose to fight crime by donning a cape and costume and secret identity. That's an established, proven method in that reality. Indeed, in the context of the stories, Batman is one of the people who proved it could be effective and thereby inspired others to follow suit. So analyzing it in terms of how it would (or wouldn't) work in the real world is a conceptual mismatch, like critiquing a magical battle in
Harry Potter on the grounds of real-world physics.
People tend to think it's so cool and smart to be cynical and deconstructive and say all superheroes have to be pathological fetishists and fascists. Maybe that was cutting-edge thinking 30 years ago, but these days it's just going along with the crowd. It's a hackneyed idea that offers nothing but negativity. Now more than ever, I think we need to re-engage with the idea that superheroes do what they do because they're
good, because they want to help and protect people and the symbolic personas they embrace can be inspiring. I think that today's audiences are ready for that, as shown by the fact that they embraced the idealism of
Wonder Woman far more than they embraced the cynicism of BvS.
So yeah, clearly Barbara is just as damaged as Bruce, Dick, Tim, Damien, Steph and Cassandra. Otherwise she'd be going to law school and/or a police academy instead of stately Wayne Manor.
In the post-Crisis version of Batgirl's origin story, she was refused by the GCPD and the FBI because she didn't meet the height/physical requirements, and Jim Gordon was too overprotective of her to let her become a cop. So that only left the cape route.
Also, Tim didn't become Robin because he was damaged. I think he was given some major tragedies later on, but initially, as I remember reading the stories when they were new, he sought to become Robin because he recognized that Batman needed a Robin to help him cope with
his damage, to be a stabilizing influence so that he didn't lose his way. Like Barbara, he was someone who was inspired by the positive aspects of what Batman did and simply wanted to help.