"Most people" wouldn't, it all hangs on whose story you land on first. Having completed the game yesterday, I can now say with certainty: Luna's story is the only one where this is a problem. Luna has the only password lock in the game that you can conceivably hit before it is revealed that the Flow screen is not merely a play mechanic (all others are in Phi's story, and they are behind a story lock).
And I......really disagree with you on the importance of waiting on Luna's ending.
[spoiler]As I said before most of Luna's ending is merely confirming suspicions. And I think, given the lack of a story-lock, the game designers were aware of this. There are just SO, SO many more less predictable elements that fall outside of her story, especially around K and the exact mechanics of how the time-jumping works. Sigma's ignorance in "prior" timelines is a non-issue since it is supposed to be a struggle for him to retain his memories; in most cases he isn't supposed to know everything the player does. For that matter, once you realize the nature of the game's story requires letting go of linear time, you basically expect that you're not going to be fed things in order anyway.
On that note, the only bonding with Luna outside of her own story that I considered at all significant was concerning Sigma's arms, and I honestly don't feel that I missed much. Most of that centers around Asimov, and as a Mega Man fan who's long been trading paragraphs with Zan, applying Asimov's laws to a non-Asimov work is something I find more than little cliched. Luna's own story pretty well communicates what a kind soul she is, Sigma's basically just lets you know how he knew to look for her in the garden, and that's pretty much it.
I don't think Luna's character or story are in any way bad, mind you. They're just oddly predictable in a game that otherwise makes it a point to screw with your expectations (not to mention your concept of reality). I mean, jeez, I knew the "016" in blood did not refer to Luna as soon as I saw it.[/spoiler]
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