"Heartbreak Hotel" was written by Hoyt Axton's mother, as I recall [At least that was what Axton said in an interview]. A lot of guys from producers to agents to rock stars got co-writing credits so writers could get their songs recorded and / or published. You'd be amazed at how many songs that showed up on Bandstand and the Dick Clark show got published by Clark's music publishing company.
As for Elvis, I would stand by my contention that despite the credits, he didn't write the songs.
That's fine. I understand, truly. I am not so concerned with the whole "who's the best popular artist" debate, because, as I have stated, there are no popular artists. There are loads of popular entertainers. Actually, I'll take that back. There is one or two popular artists, and the one that comes to mind immediately is Dave Brubeck, among the living, and Miles Davis, among those who have passed recently.
Still, the majority of people would tell they've heard those names I mentioned, but don't know what they do. Kind of sad really.