I believe that the RAI is to prepare all spells at once.
Yes - but that's not all.
To arrive at a different RAW interpretation one needs to apply rules lawyerisms such as "if they wanted to prevent partial prep, they would have said so".
And for a 3e-style rulebook, such an approach would not have been out of line.
But this isn't 3e.
The 5e rulebook uses natural language. Not formal language.
So when I tell you "for your meal, please pick three dishes from the menu" in informal language there aren't all kinds of possible interpretations, there's only one. (There's no need to say pick three and only three. Nor do you need to add three shall be the number of the counting and the number of the counting shall be three.)
Sure, you can come up with other explanations, but you're supposed to weed them out yourself - not expect the language itself to rule them out.
When we apply this to the passage about preparation in the PHB, the book essentially tells us "choose 12" or whatever number that applies.
In real life, I can use such "sloppy phrasing" because if you aren't sure, you will simply ask me to clarify. "Do I really need to choose all twelve right away?". That's what "natural language"
means - it's the language you use in everyday conversations, where anything unclear is resolved
through further talk.
But the PHB can't talk back at you.
In 3e, you should expect the PHB to come up with any clarifications, if they apply.
And - super importantly - that if it stays silent, that you did not miss anything. You weren't the PHB's friend. Anytime the PHB missed something, you were right to pounce on that "loophole".
But in 5e, you should simply use the most likely interpretation, given a trustful, non-adversarial atmosphere.
If the book tells us to choose 12 without further elaboration, this means that whenever RAW is important (which it isn't at your home game), you simply "choose 12" in the simplest sense of that term. Which obviously does not include choosing nine now and three later.
Moreover, you should not assume two different paragraphs were written by the same person in the same state of mind. The fact that the subsequent paragraph says "can" instead of "must" is a weakness in the eyes of the lawyer,
but you don't exploit weaknesses among friends.
That particular choice of wording is likely only a nod to the fact that factors can make your character have a different number of spells. Or perhaps you can't but the writer didn't want to commit to stronger language. (A very common result when you're not writing stringent, iron-clad rules language, by the way)
But none of that matters. Where you go wrong is when you confront the writer of the first passage with the second passage. Which is what you did when you found the word "can" in that 2nd paragraph, and took it, and returned to the first paragraph.
You don't do that with your friends: "You just told me you were away for six hours, but yesterday you told me you didn't leave until two o'clock and I checked our train ticket: we met half past seven. That only leaves five and a half hour. You're inconsistent and probably hiding something. Tell me now! Confess!!"
No.
Instead, when you read "natural language", you expect kind-of-sloppy inexact phrasings that you interpret in the most straight-forward way possible. (My friend remembered wrong. Or he counted wrong. Or he sucks at keeping appointments. Or he is hiding something which is none of my business.)
So when the rules tell you to prepare 12 spells you do just that and nothing else.
At least when it's kind of important, which it has become... at least in this thread.