Whether Agatha Christie intentionally copied Watson in Hastings or not, he is an example of a necessity for a successful mystery writer: To fully engage a reader, generally one has to not just present the mystery and let the reader think about it to whatever extent he feels like doing and with whatever skill level he has. That route leads to dissatisfaction on the readers' parts as not only would many not have any particular skill to be thrilled about when the end arrives, but a reader cannot direct actions or ask question of their own and many get a wee frustrated in that their theories cannot be investigated. And out of the milieu, most people read a book over time and will not be fully up to speed each time they pick up the book to continue.
Having a Hastings allows the author to pull and push the reader into active engagement. Even piking up the book after 2-3 days, the theories and... what-not... that the foils rattle on about let the reader feel his own theories are in play (they would often be precisely the foil's theories...) but the device is an active one generally engaging the reader's thinking vs. him just chunking along to get the book done.
Not to mention the ability to misdirect the reader which also keeps him engaged rather than feeling the last 50 pages were pretty thin as nothing was left but a fairly obvious idea. (That is also why so many books and shows have 40 different crimes and personal quandries solved before finally presenting a (usually) pretty obvious killer.)
So a device was needed and Watson had been a solution in the Holmes stories. Christie went that way. Watson was all those things, but Hastings being them as well wasn't necessarily in any way copying him. War service for instance: not only was WWI JUST over when Christie was hitting her stride with almost everyone not in industry having been a soldier and so any given man alive would also likely have been one, but for the person presented as her detective's foil to be above any suspicion and filled with plenty of referential authority, he had to be an ex-soldier. "Well, Poirot, I was a malingerer whilst your nation was swarmed with the Bosch, and I hid from the draft, but let's be friends, best buddies..." was implausible. The foil is meant to be US and so must be acceptable to us. Speaking of acceptable, both had to be officers for the elite detectives and society of the time to accept their company and then presence in the investigation (non-police must always have a reason for others to accept them poking into things and Christie liked her stories to develop out of her characters' lives somehow. No one just walked into an office, for instance, and hired Poirot. First you fell into his shoes whilst he was being mortal, and usually fussy, and that was a setting then for a stranger to arrive and a story to be told. So even a random appearance at his office was still something you were already engaged in. Hastings just served that purpose on a broader scale.
Two other quick points about the similarities the OP mentions. 1) Would a simple and straightforward "the husband is covered in blood and kneeling over his wife's body hammering blow after blow into it with a dagger" type stories bring Poirot to the table? No. Only difficult and far less obvious cases required him. The kind of criminal that sets the mystery book stage is actively misguiding the average person. That's what the professional (police usually) brings to the table along with expertise in the mechanics of investigation: he doesn't drop into the table-setting. He doesn't have implausibilities in the story already explained away in his head. He doesn't think someone was always present, even though no one saw him leave, just because him leaving wasn't part of the table-set story. The professional outsider isn't fooled. So yes, the stories Hastings told were obscure to the reader because the reader IS folled by the carefully set scene, and the Holmes stories along with any really siccessful detective story, are too... or again, the reader won't care much for the story and the author would go back to Home Depot's lumber department. And 2) Poirot had many other friends. They just did not clutter things. They were in Belgium and across Europe, they were in England and the reason someone invited him somewhere (the recommendation of the friend, mutual to them and Poirot). But it was clear he wasn't isolated in any way and that his company was as much desired as his presence. Hastings was simply much closer than any in England, perhaps than any at all.
Notice, by the way, that in Holmes' time, the police were not very professionally skilled at all (in fact, a couple generations before, Poe's archetype for detectives went rogue himself). Holmes himself was a nutter and while Watson was there for the very same reason Hastings was, there would have been absolutely nothing for the reader to latch onto with just Holmes. Christie's generation though, had professional police, skilled in detective work, though clearly at the start of it, emphasizing routine and such in a way organizations do when resistance to something is finally beaten down, but many would still slip in their own slapdash habits and techniques if "the Army way" (whatever, right?) weren't hammered at them again and again. Innovation being available, sort of, but not too rewarded, thinking even near the flaps of the box discouraged. She had a husband? They do most murders of women? Get him in and sweat him. But none of them buffoons like Lestrade often was. So Hastings had to provide the comic relief as it would have felt as anarchical for someone then to sneer at the police as it would have for an upstanding citizen to sneer at the police in Dragnet in their own time.
Hastings and Watson both kept the stories from being presented:
1) Basic facts requiring the police.
2) Clearly only these three things matter.
3) Two of those thing really can't be someone other than this fellow.
4) Take him away; maybe we'll see his connection to the third thing, but who cares? We aren't really wrong.
2-3 pages and all done.
There was an author from New Zealand who wrote stories in which the detective and his sergeant would be sure of the murderer an hour or two after arriving, though that would just be said ("Of course, it must be him." "Oh, no doubt sir, but proving it needs doing." No name, just "him"...). I guess enjoyable enough but a bit hard on one's sympathies for the policemen when they knew the killer but further murders occur while they let him roam about during their investigation.
The other main approach in mystery writing is to tell the storiy from the detective's mind and walk a tightrope of him going off on (um, stupid) tangents and acting on (um, kinda stupid) theories... so he is his own unskilled foil AND the elite detective. It can work: "They Call Me MR. Tibbs" is a fine example, but then often the mystery is what Hitchcock called "the MacGuffin" so... And really, in the case of Poirot, can we picture an intimate single person relationship with Poirot?
I think she never allowed that she had copied Watson because she didn't copy him. She chose him much the way he himself was chosen for the Holmes stories. He was different in that his setting was different and so he had to be, but that was in details, not in purpose. Something to engage: to hold, to push, to pull, and to prod the reader here and there was needed in each case, and both authors went the foil route, then made the foil fit their societies. So she hadn't really copied him, just chose to use that device (to which no one held patent!) and so why would she admit she had? Also, do bear in mind, much of what one "knows" of Poirot and Hastings comes from movies and TV, not from reading the books oneself. And THOSE not only had to fit them into their own societies and times, but into their own sterotypes about the characters themselves. Shaky ground for reasoning about Christie's reasons and motives. (if I were a good writer that would be "motives and reasons" as the one follows FROM the other, not the other way around).
She did do the omniscient detective quite well though, no need for a constant foil, in Miss Marple. I prefer her to even Poirot who is #2 in my listing of incredible detective characters. Those stories are magically done. Movie and TV adaptations, kind of not. Enjoyable enough, but not magic. So she could do without a foil when a foil was not the clear choice for proceeding. But Jane Marple was a much more everyday and approachable character so the "Everyman" connection was made with her and usually Christie surrounded her with people to bobble about keeping your mind percolating on wrong ideas. But Poirot's character could not have easily engaged the Everyman. Oh, he'd make any friendship available, unlike, say, Holmes who wasn't even an "acquired taste" but slowly and not in the book's time. Jane Marple? Instant. So Poirot needed an Everyman foil. And was given one. That's not the same as copying him though it did constrain his available characteristics and behaviors. Like eveolution often produces greatly similar traits in utterly unrelated beasties. Same problems to solve? Same traits, by and large, even wiht no direct relationship.