I feel like a person is missing out if they only ever listen to a band's greatest hits album. The songs make much more sense and you understand the artist better when you take the time to listen to their whole discography.
A lot of the time it also comes down to understanding the album, rather than just the artist. I believe that a good band will vary their sound from album to album. For example, if you listen to the Killer's first album Hot Fuss, it screams British indie rock, but their next album sounded like they were channeling a Bruce Springsteen-esque Americana vibe. Then the next album was like they were channeling the Americana vibe, but from space. Now their latest album Battle Born feels like an amalgamation of all those things.
I think if you're understanding the album, you're understanding the artist. By understanding the different "feels" of their various albums, you're seeing how the band is changing, what they're being influenced by, what they see as important.