The lyricist and composer are on the work as well.
A fair amount, but not as many as we'd like (so we'd like them to do it more often!). The solution is definitely not to duplicate the lyrics links on every recording of every song though, but to link the works to those recordings (automatically adding all the work data to them, like the previously mentioned composer and lyricist).
I quite doubt making people add the lyrics to the recordings (which is the same amount of work, because you have to enter the info once per recording anyway) will make them add more lyrics links. Fact is, adding lyrics links is a pain, because you need to add one link per song in whatever way you do it (and that takes ages). Not sure that's avoidable though.