Google search results vary significantly depending on your previous browsing history, you past searches and many other factors. The users' who actually perform the site evals will generally be the more active users of the site. Thus, the results that they see will anyways have the site ranked up high. However, most of the traffic that comes to a SE site is from new users or users who have not visited the site before and are performing a simple keyword search. For these users, the rank of the same page will be lower. As the point of the self-eval is to judge when and where the site turns up while searching, dont the localized results make the process not so useful?
Currently, RE.SE has a self eval going. Here is one of the sample searches :
Third result when logged into Google.
It was eighth through a proxy server.
DuckDuckGo doesnt list the question at all. It instead has a result (~15th-20th) which links to the OP profile.