You're conflating and/or confusing things.
There has ever really only been one argument: The suggestion Micheal is a canon violation or "never existed" because she was neither previously mentioned or appeared on screen is a fallacy. This goes back to the day it was first revealed she was Spock's sister.
Unfortunately, this argument devolved into "she's a bad character because her association with Spock has never been mentioned before." and the implication that not having Spock ever mention her is somehow detrimental to her existence. While this is perfectly valid subjective opinion (albeit unwarranted), my point is that she was never mentioned (I mean, beyond for the obvious.) because she was never plot-relevant, which also seems to be something you're confusing.
Plot-relevancy isn't just limited to the plot itself. It's all the stuff that turns plot into story - instead of just being a collection of randomly assembled sequential events. It's all the things that lend credence and motive to characters' actions and reactions and the things that trigger them. And it is also anything that adds thematic texture, as theme and plot are intertwined -- especially in something as thematically driven as Star Trek. Plot-relevancy is a roadmap for the audience meant to guide or even manipulate expectation. To that end, both demonstrating O'Brien comes from a blue-collar background and that Garak talks too much (which often lands him into trouble) perfectly fit the bill. And, yes, writers only ever stick to plot-relevancy, which is why scripts aren't randomly littered with superfluous trivia.
Micheal was never plot-relevant. And, like
@fireproof78 said, whether it's Micheal or Sarek or David or whomever, this holds true any way you work. The fact that Spock had never mentioned his parents before was used (besides for the cheap dramatic beat) to quantify the rift between them. But imagine this was the case and Kirk says something like "Mr. and Mrs Sarek. It's so nice to finally meet you. Spock talks about you all the time." People would run to the
interwebz fanzine shouting "ZOMG! Spock didn't mention his parents during the chess game in WNMHGB! Canon violation!!!!!1111" That sort of thing happens all the time in TV. The audience just accepts that the reason they've never been mentioned is that, up to that point, they've never been important. And despite peoples instance to the contrary, there is no matter of magnitude for Micheal.
And this is all true, even if we could somehow magically Warp 9 back to 1965 and pencil in Micheal Burnham into Gene's show notes. Assuming all the shows play out the same, there's nowhere to put her that wouldn't feel forced and out of place. This includes Babel. Having Amanda shout "Why can't you be more like your sister?!" during their argument adds nothing to the story and just lands WTF face on the audience. That does not mean, however, Spock didn't ask about her off-screen while they were laying in the med beds. We have no way of knowing and it's illogical (See what I did there?) to assume one way or the other.
What does it say about Spock that he never discussed Sybok? Well, his father had a failed marriage and a son who contradicted everything Vulcans apparently stand for (T’Pol treats those emotional Vulcans like deviants in Enterprise). So I can understand him not bringing up Sybok.
What does it say about Spock that he never discussed his human sister who was also in Starfleet *and* a science officer who *also* tried her hardest to be Vulcan despite being human (very similar to Spock)? Did she embarrass him? Why? Was he ashamed of her? Did he never see her as his real sister? Was he totally indifferent to her? Did he secretly love her, explaining his spurning of poor Nurse Chapel?
And this right here is the crux of the matter.
It doesn't say anything about Spock. You're making assumptions and drawing conclusions based on facts not in evidence.
This is like, during his closing, a prosecutor arguing the defendant is guilty because he doesn't love his sister -- a sister who was never a witness, never mentioned in testimony, and never described in any document entered into evidence. This would get the prosecutor into hot water, even if the sister was sitting in the gallery.
We can't make any assumptions about their relationship or even how ell Jimmy knows her. Think of it this way: Spock and Kirk's [on-screen] relationship spans well-over a quarter-century, yet, of all that time, only about a year (if even) is depicted on screen. We have no idea how well Kirk knows Micheal. It's very possible they're very close friends. But until something appears on screen, it's irrational to assume one way or the other.
also it doesn’t look like my point has been quoted correctly here - had me confused and looking back at what I’d written 
