Midchuck , yes, songwriters are often delighted to have well-known performers 'steal' their songs (e.g., be thought to have written them) when that brings the song to national or world-wide attention and brings in the royalties.   Sometimes, as in the case of "Blue Moon Of Kentucky" or Carl Perkins's "Blue Suede Shoes," the original songwriter & performer even adopt the new arrangement & styling brought to the song by the new recording artist.   (Kris Kristofferson probably feels just fine about what Janis Joplin did with his "Me And Bobby McGee.")   
Nevertheless, I still think it's important, when possible, to remind people who it was who actually wrote the song.    It's one thing for the general public to sort of assume that the recording artist wrote the song, but when you're posting song lyrics online or in a song sheet, if you don't really know who wrote it, I think it's better to leave that line blank than to just put in the performer's name as composer/lyricist.
I think it's very helpful for people to be able to find the accurate songwriter credits when they want them. But sometimes that's very hard when the internet, for example, is so full of wrongly attributed song lyrics.