Why lock anything in until it needs to be, though?
Because then the player can build off it, as can I-as-DM should I want to and-or have to.
I mean, if a player says to me "My PC wants to find their brother who left the farm years ago" I'm going to incorporate that into the game. How will I do so? Why commit then and there at session zero when I can see how the game goes, and see if there's a way to incorporate this into the ongoing events in an interesting way"
Depends. If we've already determined that the PC doesn't have a brother then it doesn't have a brother, and one would hope the player is already well aware of this (having been involved in the determination process) and thus won't try to invent a brother where none exists.
If we haven't yet determined the makeup of the PC's family then I'll keep this in mind, and maybe bring it in later depending on some other factors e.g. is the player doing this just to try and hog airtime, is the player actively trying to incorporare other PCs into this side-story, and so forth.
Ramifications of what kind? I mean, I get the idea of alignment and all, but I don't tend to think that people only ever behave in one of nine possible ways. So how do you decide when ramifications are needed, and what they would be?
I look for patterns.
Ramifications for most characters include how an aligned item treats you; what results someone gets from casting Know Alignment or Detect Good/Evil on you; how you're treated by some NPCs if-when word spreads, and so forth.
If you're a Cleric, Paladin, or other class with alignment restrictions the ramifications can be much more significant, up to and including loss of class or - in very rare instances (i.e. once in my DMing career) - a divine bolt of lightning dropping from the sky...
And if someone's Chaotic Neutral, how do you ever determine if what they've done is against alignment? If they become too consistent?
As CG and CN are the two most common alignments played here, I've had lots of practice with this one.
They might become too consistent or predictable, or insist on following/enforcing/inventing rules and regulations, or (for a CN) consistently act evilly or goodly, and so forth.
I don't think I'm quite following.....Bob and Mary had a fight in real life, and so they have their PCs fight in the game?
In this example, yes.
You'd be more mad about that than if they just decided their PCs now wanted to kill each other? I mean....what's the difference? The same thing is happening.
The difference is the meta-thinking and motivation behind it.
If their fight in-game mirrors their fight in real life (and-or is caused by it), that's just the reverse of having an in-character argument move out of character; which is something I smack down on rather hard.
But if their in-character fight is simply something happening in character and nothing to do with real life, I'm cool with it as long as it stays in character.
Two people who live in the same town bumping into each other in that town is simply not implausible. Bumping into the Pope in that town is probably a better example.
Well, maybe not, as the Pope's movements outside the Vatican are usually quite well publicized.
But e.g. bumping into Tom Hanks or Taylor Swift were either here on an unannounced vacation, perhaps that's closer to what you mean.