I think the perspective is very valuable. When Trent wrote the song, he was still young. It gives time to atone, to grow, to do better. When Cash covered it, it was near the end of his life. He doesn't have the luxury of time to make up for his shortcomings. It's a lot more fatalistic.

To answer your second question, no. I don't think it would be as big without his name attached. Johnny Cash was so big, so iconic, that of course anything attached to him would get more attention. And the fact that more people are familiar with his life story and why this song would resonate so deeply with him definitely helped to spread the cover as well.

To answer your unasked third question, personally I prefer the original. I do appreciate Cash's cover though, and am glad he made it.