However I think being able to say "I (co-)wrote this" also plays a part - especially in Elvis' time, actual singer-songwriters were probably held in greater est

However I think being able to say "I (co-)wrote this" also plays a part - especially in Elvis' time, actual singer-songwriters were probably held in greater esteem than artists that were just "parroting" songs others wrote for them, so giving the impression that they were involved in writing the songs may have been important from that perspective too...