LAME is a really great example of why patents exist: the need to avoid the mp3 patents resulted in the development of technology that was superior to that covered by the mp3 patents. Do people really think LAME would have been developed if people were just reimplementing the existing mp3 encoder?
This is wrong in so many ways I'm not sure where to start. LAME was covered by the patents, so your whole idea is backwards and even if it weren't it's not supported by any evidence - there's just no relationship between patentability and how many encoders get implemented independently or not.
