What I mean by that is Neo wasn't the only one to have the potential to become the One. In The Matrix, we see that some children already possess powers.
It's clear that they exhibit powers, and that the hackers aren't sure whether they are The One or not--but I'm not aware of anything that unambiguously clarifies that any of these children can be The One.
I'm not not sure I disagree, but I'm also not sure how we can distinguish between someone ~randomly becoming The Anomaly, and The Anomaly always being the same person.
And if the machines need this prime program at a precise moment, why give it to a human to carry and then disseminate? Why not just keep it on a hard drive and use the program when it is time to reset the Matrix?
I doubt there's a satisfying answer to this, but I don't think there is a specific moment where the machines need the prime program. I read the films as suggesting this as circling back to the problems of choice, and of subconscious consent. Choice is the problem--and for it to exist, someone has to be able to make the choice the machines are engineering against.
In the timeline we're shown the machines do need Neo, but that's because of Smith--and Smith only exists in his current condition ~because of what happens to his program after Neo "destroys him in the first film. (I'm basing this somewhat on the scene after Neo's fight with the "upgrades" earlier in the second film, where Smith tells himself that it's happening just as before--with a knowing look that signals that the Smith copy is the exception. Also on the fact that the machines have no apparent countermeasure for this happening to Smith.) There is presumably still the "escalating probability" problem, but I don't recall anything that clarifies when/where/why that would finally become a problem for the machines.
That is why it is my general belief that Neo's prime program is self-generated by his life experience and the amount of knowledge and elements he learns through his journey.
I don't think there's anything to unambiguously decide this one way or another. My personal inclination is to say that we have to "trust" the monitors that the architect shows us--that when the previous-Neos respond, he is showing us past-realities and not a metaphorical abstraction to make sure Neo is smrt enough to recognize "himself". This isn't the same as thinking it's implausible that it's working this way. Just that I see that as being on the other side of a decision razor based on what the Wachowskis elected to actually show us...
It even makes sense, given the fact that all the other Ones chose the door to the Source; they basically repeated the cycle, because their experience toward humanity and LOVE was very generalistic. Neo's experience, as the Architect so elegantly put it, is "far more specific vis-à-vis love". That is what separates him from the others; it is what makes him choose the other door.
Note that the Oracle plays a role in this. She tells Trinity that she'll fall in love with The One. Given this, I'm not sure there's any clear evidence that the distinction between iterations must lie outside of the Matrix.
Then there is the dissemination of the code which is also different. The arrival of an enemy like Smith, which threatens the machines and the humans neo can break a truce even a peace accord should he defeat Smith.
Now there is two-element that needs to be taken in account for this last part:
Neo, when first destroying Smith, left an impression on him, quite literally (see the speech of smith in The Matrix reloaded, before the fight between him and Neo, after Neo talked to the Oracle.)
At the time of the last fight, Smith has absorbed everyone in the Matrix.
Hence the ending; Neo let himself be absorbed, i.e. his code joined the network created by Smith, which in this case equalled everyone in the Matrix, hence the dissemination of Neo's prime program, which is different from others due to love, changing the usual reset of the Matrix for two reasons: the prime program is different, and Neo broke a peace accord right before.
I'm not sure this holds (or is the difference). This Neo chose to return to the Matrix instead of to the source. It isn't a given that Smith absorbing him is the same as disseminating his prime program. It's also not a given that his prime program is at all changed by love. (And I guess this clarifies that either Neo's prime program does not actually prescribe the whole "choose 23..." bit, or that this doesn't trigger its dissemination).
None of that would make any sense if Neo's prime program was a static code, or a program given to him by the machines.
I've weighed this a bit, but I'm not really sure. "A static code" very much fits how most people thought of code when the movies were released, but the oracle does ambiguously refer to programs "breaking down", which implies that either their code, storage, or hardware is subject to some kind of change or entropy. I've never quite known what to make of this statement in context. I've assumed it's vaguely metaphorical, but I'm also unhappy with that as a conclusion.
I mean, the biggest plot whole would be why give him the code in the first place; why not just keep it and use it when needed?
Not that this isn't a fair question, or that I personally find this answer satisfying, but in-universe I think it is: they give it because Neo has to make a choice.