Now please ignore all the trainers who in the past have caught one, especially the NPCs. Their Battle Facility teams don't exist in canon, why would you think it does?
Because the other trainers in the Battle Facilities are top-level trainers, equally or moreso skilled than the player at Champion level. There's no reason that they wouldn't be able to meet and capture legendaries, especially in light of things like Latias' dex entry referring to it living in "herds".
And when facility bosses canonically use legendaries, there's even less reason to say that minor NPCs can't or wouldn't. One NPC outside the World Tournament building in B2W2 makes reference to using Lunar Dance in battle "on rare occasions" which might be just as simple as her occasionally using it via Sketch or Metronome but in context seems more like a wink to the audience to say "yep, I have a Cresselia." Steven is shown to have some sort of friendship/affinity with the Lati species in ORAS. Less serious examples include an NPC in Alola who exclaims that he just got a Mewtwo via a Wonder Trade, though this one is more Rule of Funny than anything else (and I guess also clues the player in that they can trade legendaries if they so choose).
As for why scientists don't know about the bird trio - it's inconsistent, but in their debut generation legendaries are often afforded an air of mystery and uniqueness. None of the Alola legendaries are used in the Battle Tree; Uxie, Mesprit, and Azelf aren't used in the Gen IV Frontier or Subway; the Johto trio aren't used in the Battle Tower in Gen II. The story they wanted to tell around the bird trio is that they're unknown; if they're included in future generations, they might be less fabled.
But why do you assume this is the case for all legendaries? In the case of the Regi species, for example, it's pretty much confirmed that they have been studied:
Regirock
Regirock's body is composed entirely of rocks. Recently, a study made the startling discovery that the rocks were all unearthed from different locations. (Sapphire dex entry)
It is entirely composed of rocks with no sign of a brain or heart. It is a mystery even to modern scientists. (FRLG dex entry)
Regice
Its entire body is made of Antarctic ice. After extensive studies, researchers believe the ice was formed during an ice age. (Emerald dex entry)
Having a legendary isn't something you'd expect most people (particularly serious trainers) to shout loudly about, but Drayden's comment in Gen V that "if a Pokemon didn't want to be with a human, it would simply leave" cause me to think that in the event that a legendary Pokemon partners with a human it's pretty much at the Pokemon's discretion, as in the case of Noland and Articuno in the anime. The fact that in-game they're part of your team like any other is just gameplay and story segregation. So it is perfectly plausible to me that many legendaries simply do not want to be studied and that anyone who pushed their luck too much by trying would find themselves very quickly abandoned.
And research almost certainly is ongoing on some of them, but research is slow. Think how little progress gets made even on topics we know a lot about. If the Galarian bird trio are a relatively recent sight (even if "recent" here means the last 40 or 50 years) then yes, it's plausible that little would still be known beyond the observations and stories that typify legendaries.