That's a clever idea, but I think that most users would be disconcerted by the sheer amount of information that's collected by most web sites already. It would raise the question, "why do you need to collect all that?" before anything else. Which is a good question to be sure, but probably not the one that most companies want to be answering.
You're probably right about the web site getting the wrong kind of attention from this. I can almost see a government organization doing this instead, either as a public service or after some open information law is passed in reaction to public opinion on NSA surveillance.
The U.S. government might just be bureaucratic and fractured enough.
