See how that works?
No, I don't agree. Anger at harassment and injustice isn't juvenile. Use of jargon familiar to her audience isn't juvenile either. Although I can see why others would see it that way.
apparent unwillingness to learn about them
I do agree this seems apparent.
To a point where it makes her seem unsuitable to voice an informed opinion about it
I don't know enough to judge.
1) Get the videos removed. 2) Potentially get real-life identifying information in order to enact a campaign of harassment. I would hate for GWW to be harassed. She is a breath of fresh air.
The DMCA is fine when the complaints are legit. This penalizes both YouTube and the content creator.
You put the details of your legal representative on that form.
As others have noted, this form doesn't need your personal information, so no I don't agree that this is an "exploit". You never have to give your personal information.
The situation reminds me of people who make anti-Scientology videos and then cry about freedom of speech when the cult's legal juggernaut descends. Is it fair to get a DMCA or lawsuit threat just because someone disagrees with your content? No (assuming you did not violate copyright protection laws). But getting bit by a shark because you're wading in its pool isn't fair either - just inevitable.