Why do you care if people quote?
Because the twitter system integrates notifications automatically when users retweet mentions or save it as favorites. But if users quote mentions, twitter system notifies it individually. That's the first reason why I prevent people from quoting.
And second reason is about copyright. I have the copyright on all images I upload. If I allow people to quote them, the possibility of copyright infringement problems might increase.
These two are the major reasons that I do not allow to quote my tweet:)