Thanks for the suggestion. Part of the reason we don't do this is the returned search results on Google are Google's commercial property. To use them in such a capacity would require us to reach a commercial agreement with them. These agreements come with stipulations that we don't feel represent the privacy interests of our users, so we don't pursue such agreements.
The other reason, is because of the 'filter bubble' Google tailors results based on user tracking, which is what helps with result accuracy. So the results we as DuckDuckGo see on a query would be different than what you see. Plus, even if we could see your results, we wouldn't want to. We don't think it is good to be filter bubbled, we want to serve you the best results we can without censoring you. It should be your decision to a view a certain website, not ours!
As a DDG user I'd be really happy if you did this and think it would be the best way of identifying searches I'm unhappy with. I go to google now only if I'm not happy with the results from DDG.
Don't believe for a second that governments are not already banging at the door for access. The only ways to combat is either hosting in neutral offshore datacenter and incorporating there and living there is to not collect "useful" information in the first place on users. I think they went for the latter.