I have replayed all the Final Fantasy games at least once to completion. There are little things that can be done to make the gameplay more interesting even though the story stays the same, not to mention that with several of them you can do different things to make the story slightly different in some places. Otherwise, it would just be like watching a movie repeatedly, which gets old no matter how good the movie is.
But I do understand what you are saying about the good scenes that will always happen when you play the game, seeing them for the first time is always the most remembering experience. In FFVI, the opera scene was very touching the first time I saw it, but any subsequent time, while the scene is still good, it just didn't do it for me like it did the first time. I remember playing FFVIII and watching (SPOILER)Rinoa float through space on the verge of death, thinking that she was going to die. That scene was set up very very well, with the horribly sad music that was playing in the background, the juxtaposition of the several things happening at once in that scene, and actually not knowing what was about to happen, that scene brought me to tears the first time I saw it thinking that (SPOILER)she was about to die. Honestly, I have played FFVIII a good ten or twelve times and have not gotten bored of it yet, but some of the scenes just aren't the same after the first time. Although the scene with Laguana at the end still gets me sometimes. The end of FFX was one of the sadest things I've ever scene in my life, very very well done. I remember I beat FFX with my friend Michelle, and we both ended up using about half of the box of tissues, it was just sad. I have beat FFX a few more times since then, and while it was still a very sad and touching scene, it just didn't affect me like it did the first time. I have more examples, but I think that will do.
The major events (except in FFX-2) will always happen the same, but there are a lot of minor events in all of these games that you can manipulate to make the story slightly different, and in FFX-2 you can actually manipulate some of the major events. Playing the game through again, knowing the story, allows one to see things that they didn't see the first time, which is reason enough to play most of these games over. That and different styles of doing the battle portion of these games. In FFX-2 you can actually have a different story to the game. No matter what road you take it will end up in one of three places, but you can take a different road each time, which I liked. So while the major events are lessened and spoiled after your initial playthrough, there are enough in these games to keep my attention through at least one more playthrough, if not several.