I discovered this old thread that I didn't follow up on, and thought I'd expand on my ideas a little. To me, the word "cover" implies that performing songs you've written yourself is the norm, and performing songs written by other people is an anomaly. This is the exact opposite of what traditional music is all about.
This attitude encourages a lot of really bad songwriting, when there are lots of perfectly good songs out there which neophyte singers could sing with much better results. In my opinion, substandard singing (especially when due to inexperience) is much more tolerable than substandard songs. Substandard singing *plus* substandard songs can be excruciating. Neophyte singers should be encouraged to sing good songs from other writers rather than trying to write all their own stuff right away.