To me it always sounds like the speaker wishes to sound smart. Not that Harry isn’t intelligent; I agree he probably has New Daddy nerves.
But is it? That’s what I’m curious about seeing evidence of. I’m a descriptivist when it comes to issues of language, and have a healthy respect for style rules in formal situations, but I’ve never gotten the sense that this usage is standard in prestige dialects: in fact, I’ve been taught quite the opposite by what you may call strict grammar prescriptivists. I feel it’s a more colloquial usage – which is fine by me – but the grammar police are going to pounce on you for it.
Though please keep in mind no grammarian I.
Actually, Merriam-Webster agrees with you to some extent.
Bolding mine.
In this sense, Harry is referring to Meghan and himself;) as the object of the announcement.
I don’t think that it has anything to do with being a “prestige dialect.”
Something along the lines of “Meghan has delivered our baby boy today”, which leaves no doubt about sirage (is that a word?).
I thought it was the doctor who delivers a baby.
Perfect cite. I was thinking of Emily Dickinson, for some reason, when it came to this usage, so interesting that her name turned up–perhaps I had read about this years back. Now, which “turn of the century” is meant? 1900s or 2000s? If 2000s, then that would coincide with when I remember this usage popping up, but maybe it’s because I’ve noticed it more because critics were chirping about it more. That said, I do swear I remember that usage was frowned upon when I was in high school and college, so perhaps 1900s is meant there.
“Meghan has been delivered of our baby boy today.”
But seriously, there’s absolutely nothing wrong with how Harry phrased the announcement.
I’m sure they must have been referring to the turn of the previous century.
Given the fact that some people are mildly bothered, one way or another, by it, I would say “absolutely” is not really the correct word to use here. Yes, the bothered are basically inconsequential, but they exist, so the utter lack of wrongness is not absolute.
So, should there be a horrible tragedy ending in Harry’s coronation, would this use of ‘myself’ be considered the King’s English or would it still be considered an error?
The fact that something bothers someone doesn’t make it wrong.
“Meghan and My Royal Self?”
I’m not even going to attempt to do an actual diagram of the sentence on a computer, but let’s break it down to its building blocks.
“I’m very excited to announce” - no problem there.
'that" - Announce what? “That” serves as a bridge. In fact, the sentence would be just as correct grammatically if Harry had left the word out entirely.
“Meghan and myself had a baby boy this morning,” - now we clearly (that) see this is an adverbial clause answering the question “announce what?” And adverbial clauses have their own subject and predicate, even though they modify/describe/explain the verb.
“a very healthy baby boy.” - What kind of baby boy.
Grammar tells us that adverbial clauses take a nominative pronoun (“I”), rather than an objective pronoun (“me”) and certainly not the reflexive pronoun, “myself.”
In any case, congratulations to the happy couple. I certainly won’t pick that nit with them, self-wise.
If he were really being royal, he should have used the “royal we”: “Meghan and we had a baby boy,” or “Meghan and ourselves had a baby boy.” 
I listened to the entire statement from Prince Harry, and later on he made a grammatical error and then corrected himself. So I’m putting it down to his obvious excitement and stumbling over his words a bit rather than any formal decision about grammar.
Of course, had he been speaking in the vernacular he might have said; “'Er indoors dropped the sprog this morning; anyone fancy wetting the baby’s head?”
Frowned upon by prescriptivists. But outside of certain fields where it’s required, such as editors and schoolteachers, prescriptivism has been mostly dead within Modern English for over a decade.
Well, yes. That’s what I was wondering about: whether the usage has become accepted by the prescriptivist grammarians. I mean, those are the only ones who “frown upon” colloquial usages. (I mean, yes, there’s ungrammatical structures in descriptivism, of course, but usually these arguments are all about prescriptivist grammar.)
I don’t know what you mean by “prescriptivism has been mostly dead within Modern English” for over a decade. Prescriptivist grammar is alive and well, from what I can tell. I haven’t noticed any sort of shift in the last two decades. People still get pissed off over shit like “literally” being used as an intensifier. Nothing has changed. The people who like to bitch about language usage and how we’re all heathens who don’t respect English still bitch about language usage. And printed works still have style guides that govern the use of English prescriptively and give consistency to a work.
Those are just people bitching, rightly or wrongly (but usually wrongly), about whatever their pet peeves are. But the authorities, such as we have them, aren’t nearly as prescriptivist as they were 10, 20, 50 years ago. Practically all of our non-specialized dictionaries are descriptivist now.
Style guides are just that–matters of style. They’re prescriptivist, sure, but that’s one of those fields where prescriptivism is necessary. The fact that there are so very many guides with differing styles is one measure of the decline of perscriptivism.
(Though I will grant that much of the matter in those guides concerns punctuation and citation rather than usage.)