From what I have been seeing and reading, many in the press have been rather gnarly toward H&M, and particularly toward Meghan for much of her pregnancy, which is rather unforgiving. I doubt the Sussexes feel any action they take will change any of the negativity in many quarters. Nor do they likely feel a need to use their first born to 'turn anything around' with the media.
Therefore, I tend toward agreeing with your latter arguments against:
Exactly. Although, I don't think appearing in public hours after giving birth would be a problem for Meghan, just as it certainly wasn't for Kate (what with all the care and backup available for them before, during and after giving birth). In any case, Harry and William are both known to be disinclined to be generous with their families' privacy. We have seen so very little of Prince Louis, for example. As the third child and second son, that's a situation that will likely continue. Contrast the memorable video of Prince William at around three with toddler Prince Harry banging on the piano at home with their parents vs how little we've actually seen of the Cambridge children inside their home (practically nothing except for the famous photo of Prince George in his white bathrobe greeting President Obama).
I am also reminded of how the much more obscure and little known among the mainstream, Prince Max and Princess Angela of Liechtenstein, closely protected their only child's privacy. There are public pictures of their son Prince Alfons when he was around 4 or 5 years old. But then absolutely nothing after that until he was around 15. Alfons will celebrate his 18th birthday on May 18, 2019.
https://www.townandcountry.ph/peopl...la-of-liechtenstein-facts-a1867-20180227-lfrm
Unfortunately Louise was a whole month early, due to placental abruption. Edward was out of the country at the time and missed her birth. 
