“If you surf anonymously or if you delete cookies automatically every time you close the browser, websites will ask for that permission again and again, and it will soon become very irritating to click the same I agree buttons every day.”

The extension doesn't claim to delete cookies (and GP doesn't suggest that it does), but it's clearly targeted at people that are using technological means to deal with the problem rather than clicking "pretty please don't track me" and hoping for the best.