Sure, people can get single-minded about trigger warnings and take them to a point where it's ridiculous, but that's true of pretty much anything. I would prefer calling them content warnings, just because a trigger warning almost seems to suggest that people should be triggered by it, but otherwise I think it's valid.
She says that the onus should be on the viewer to avoid content that they don't want to see. Absolutely! Content warnings are how people do that. It's not reasonable to avoid the Internet entirely, and it's not reasonable to just avoid certain sites because many websites these days cover such a broad range of topics. Trigger warnings aren't about restricting speech because you still get to say whatever you wanted to say after the warning.
If I were to create content that dealt with issues that people might not want to see (either because of trigger issues or NSFW issues), and that's not clear from the title, I would probably put a content warning at the beginning. It would just be a little courtesy that wouldn't take much effort. If I didn't put such a warning in, and someone accidentally sees something they don't want to see, then to avoid that in the future they would probably stop viewing any of my content, and now I permanently lost a viewer.