Obviously it all depends on what Legendary we're talking about (and of course they'll have to be different from the ones Ash have met since a few of those were telepathic hinting they were a bit more special).
- Believable: Kanto Bird, Johto Beasts, Hoenn Regi (+ Galar Regi), Eon Duo, Deoxys, Cresselia, Heatran, Regigigas, Phione, Darkrai, Shaymin, Swords of Justice (+ Keldeo), Meloetta, Forces of Nature, Magearna, Marshadow, Zeraora, Meltan family, Kubfu family, Zarude
- Reaching/Needs Good Excuse: Mewtwo, Mew, Ho-Oh, Lugia, Celebi, Jirachi, Lake Guardians, Manaphy, Victini, Genesect, Diancie, Hoopa, Volcanion, Type: Null family, Guardian Deities, Cosmog family, Necrozma, Ultra Beasts, Galarian Kanto Birds
- Unbelievable: Groudon, Kyogre, Rayquaza, Dialga, Palkia, Giratina, Arceus, Zekrom, Reshiram, Kyurem, Xerneas, Yveltal, Zygarde, Zacian, Zamazenta, Eternatus, Calyrex & Steeds
To explain some of my thoughts:
Deoxys: There are multiple Deoxys and it just seems like luck if one lands on Earth. Whose to say one didn't somewhere and was caught? Heck, could be used as a good "alien conspiracy" gag. No, the government/space program isn't covering up an alien encounter, it was just a Deoxys.
Regigigas: This is borderline, BUT if someone got the other Regis I wouldn't raise an eyebrow against them having searched for a Regigigas.
Shaymin: There's plenty of them around. Sure, you gotta let them migrate, but there's nothing saying they can't come back.
Swords of Justice: Now, these can't be the same Swords of Justice that Ash & co. met which were telepathic, those seem to be a special group semi-serving a Kyurem. But I don't see why there can't be others who aren't serving a higher Legendary but more on their own so are a bit more "wild".
Mewtwo, Type: Null family, & Genesect: Like, you need a secret lab and ethically questionable scientists (or it being a government secret project), BUT I could see more being made.
Ho-Oh & Lugia: Now, we've seen there's more than one Lugia and upon seeing the other Lugia it never quite felt "out-of-reach", so why would it's counterpart Ho-Oh be? Still need a good excuse, and it would more likely just be a "befriended" situation rather than a "captured", but I'm open to the idea.
Celebi: Like, it's a seemingly immortal time traveler, what does it care if it spends a few decades with a human? Would be a fun experience, will just need to contact a past/future self to check on the forest its protecting.
Jirachi: Honestly the big problem with it is that it goes into a cocoon to sleep for a thousand years (oh, and it has the reality breaking power to grant wishes). BUT if say the Poke Ball can delay the metamorphosis and without the sleep doesn't have enough power to warp reality, eh sure.
Lake Guardians: Now there would seem to be only one of each just like the other Spacetime Dragons, BUT part of me thinks there could be others due to their roles. One, they're meant to spread the capability of feeling emotions, understanding knowledge, and having willpower; for them to do that for a whole planet seems like a bit much for just three all in Sinnoh; maybe Arceus planted several around the globe at key points. Also, they're meant to bind the Spacetime Dragons if they get uppity, may want to have a few spares around if something were to happen to the most convenient trio.
Manaphy: Sort of in the same boat as Shaymin but there seems to be less Manaphy around, probably due to many not fully forming from being a Phione.
Guardian Deities: Another group you'd think there would only be one of (at least per dimension), BUT we don't really get much lore on them besides being worshipped as the guardians of Alola. So I'm willing to leave it open there could be other members hopping about other islands and fitting locations and the ones in Alola are just either extra special or the "main ones" at the moment.
Necrozma: I feel there could be more, it is an (semi?) Ultra Beast so we may just not know its home dimension.
Ultra Beast: You just need an Ultra Wormhole to open up and drop one in... very very very (many "very"s later) VERY unlikely... but you can't really say not impossible.
Galarian Kanto Birds: Now, they're probably super rare if not one of a kind... but that doesn't mean they're any harder to capture than the normal Kanto Birds. Heck, who knows, maybe they'll have Goh catch all of them.
And the remaining unbelievable Pokemon are because they're essentially deities being super powerful and/or one-of-a-kind (or close enough to it).
Well, uh, I think it's safe to assume the Kyogre option is out... but the Latias could maybe be an option. Ash has Melmetal and Goh has Suicune, so main characters are being allowed to have Legendaries now.
Sorry to hear that happened.
