Personally, I try to avoid the term "cover". Writers write. Singers sing. Sometimes one does both. I would suspect that writers like to have other people sing their songs. That shows appreciation for someone's creation and usually means money in the pocket. But, there are occasions when songs become identified with a particular singer because a singer does an unforgettable performance of the song. I look forward to hearing various singers versions of good songs and do not think of songs as being "owned" by one person or group although I am sure publishers think otherwise.