As the title suggests, I believe that since we have positive trophies such as 25 trophy points for 100 likes I think we should also have the same the other way around. So for every like rating trophy achievement there should be a dislike trophy achievement e.g. 25 trophy points for 100 dislikes etc and the same for 10 and 1000.
It shows you are active in the community. People who say no support should probably think deeper than "Oh but their dislikes they are bad this idea is bad"
If you think about it, it would prevent people from abusing the dislike button. Why would you want to help someone you hate get a trophy?
They would most certainly use likes instead. Also I don't believe you get the trophy if the the ratings are removed.