It was a marketing strategy for pop music in the last century, collectively launched by the record companies and their DJs, aimed at teenagers who indeed were made to think the person depicted on the cover was the author. Or rather, the concept of authorship was not known at all and did not seem to matter, the song was just identified with the "star". If asked for the participle to go with "by", teenagers would (usually correctly) answer "sung".

Nowadays, the kids don't believe in Santa any more. There used to be "scandals" about "singers" who actually didn't sing – this no longer worries young people at all.