I think the thing that makes the live staples fun for me is the energy of the crowd. When a band plays a deep cut from a one of their less popular albums, there are going to be people in the crowd who love it, but there are also going to be people in the crowd who hate it, as well as people who just don't give a fuck about it, and potentially even a few people who have never even heard it. On the other hand, when a band lays a live staple and traditional fan favorite, yes, there are going to be some people who are sick of it, but the vocal majority are going to be singing along and rocking the fuck out, and that energy makes for a great experience.
For example, when I went to see Iron Maiden, I know there were people in the audience who had been to hundreds of Maiden concerts and were sick to death of hearing Fear of the Dark. You know what I would say to those people? 'Tough shit.' It was my first time seeing them, and I would have been severely disappointed if I didn't get to experience FotD. There's a reason they keep playing that song - it's an amazing audience participation song, and it makes for a wonderful live atmosphere.
Same thing goes with some of the Metallica staples for me. Even if they aren't necessarily my favorite songs, I'm going to love the experience, because I'm going to be surrounded by a sea of people who are loving it.