Overall about 12% of traffic arriving on our sites is anonymous, however day to day it can vary between 5% and 20%. Should the anonymous traffic from Google remain a minority then its not really a problem.
For our clients however it has renewed interest in building and structuring sites for Bing. I don't think Google needs to do much now to outrage web masters!
Personally I still struggle to understand why Google considers the query term to be private information! It seems to be as logical to me as refusing to use your indicators while driving as it violates your privacy.