Yes. The Back Stories matter.
At the end of the day LOST is story that is about "spiritual progress" via saving the Island, as it houses "life extension" on every conceivable level. It also was then about people lost in their lives and lost in terms of not knowing the whole truth about what the Island is...
To be able to answer this better, I will have to lay out my interpretation of LOST's ending....
My interpretation of Lost ending is that the Island is a space-time machine that houses "the heart" (Ancient Egyptian concept = collective conscience) or really all manner of existence ("Life, death, and rebirth").
So I think the idea is that there are always other corporeal timelines (other incarnations of characters and events) and those are the of things we see parts of through out the series, but don't get full explanations for (like all the ways Charlie had died in other lives, different versions of Chang's tapes, a different version of 1996 in The Constant, John Locke 2007 switch out, mice maze knowledge, why we have alternate reality tie-in media, ect) and that the Flash Sideways is an ethereal/astral plane which is what "death" is. (The characters also move on by passing through light, a common motif used in relation to time travel).
The beginnings of the FS pseudo-show the upcoming 2004 of next time line they created when they time traveled back to the 1970's this time around (they basically make a branch off when hey time traveled).
In the FS they have to remember the past to understand the upcoming future they made (next incarnation/time line). This is basically "dream logic" like in Alice in Wonderland (a reoccurring reference).
For the group that "moves on", they will not have to directly deal with the Island in there next life as the FS shows (instead they will DIRECTLY in each others' lives), but for others, they will have to confront The Island again. It's why Ben doesn't choose to move on, because he believes he hasn't done enough to "deserve" the outcome the FS presented to him. This was all about spiritual progress: "It only ends once, everything before that is just progress" = life never ends as long as there is an Island with it's light-water in tact-->infinite life times/iterations of time lines...**
The reason my interpretation matters, is because as a story that's mostly about spiritual progress, in which the Island facilitates or "runs" (see also Valenzettie Equation = axiom or calculus of Island working to not "break down" fabric of universe) life, the reason the characters' backstories matter is because of all of the connections between them as people, and with places and things, AND also, because there were degrees of separation (other people) between them outside of the Island life (that no longer existed in the new 2004 the FS shows) was metaphysical proof of what the Island is and how the Island generally works, being the thing that is bigger than everyone else.
In addition it was a wonderful way to tell an epic story.