This is a great point, and something I often wonder about as well. I think it's reasonable to think that only a compromised site or site run by someone with ill-intent would pose any real risk. And in such a scenario, it's going to get out pretty quickly that the site is compromised/dangerous.
While this doesn't help that theoretical set of initial victims, it just doesn't feel like a credible risk worthy of too much worry, especially for information from higher profile sites with reputable backing.
Perhaps the solution here is better mechanisms for validating what a script can do - "script is attempting to access xyz, allow? y/n".