I think Dazzling Gleam is a strange one.
You have approximately like half of the psychic Pokemon able to learn it, but why doesn't the other half learn it?
What makes a psychic Pokemon able to learn Dazzling Gleam , and what makes a psychic Pokemon not able to learn it?
I hope it's because they knew Gengar would be OP if it gets Nasty Plot.
I'm pretty sure this was brought up before, but it's still an interesting case. So out of bored curiosity I dexsearched the Psychic-types who don't learn Dazzling Gleam on Showdown:
Arceus-Psychic, Beheeyem, Beldum, Bronzong, Bronzor, Bruxish, Cosmoem, Cosmog, Cresselia, Darmanitan-Zen, Deoxys, Duosion, Elgyem, Espurr, Exeggcute, Exeggutor, Gothita, Gothitelle, Gothorita, Grumpig, Hoopa, Inkay, Jynx, Latias, Latios, Lugia, Lunatone, Malamar, Medicham, Meditite, Meowstic, Metagross, Metang, Mewtwo, Mime Jr., Necrozma, Oranguru, Oricorio-Pa'u, Raichu-Alola, Reuniclus, Silvally-Psychic, Slowbro, Slowking, Slowpoke, Smoochum, Solgaleo, Solosis, Solrock, Spoink, Swoobat, Unown, Wobbuffet, Woobat, Wynaut.
Ruling out those that get Psychic-type as a form (Silvally and Arceus are counted here), jokemons (Wobbuffet), and Pokemon that have a limited movepool as part of their gimmick (Beldum) leaves us with:
Arceus-Psychic, Beheeyem, Beldum, Bronzong, Bronzor, Bruxish, Cosmoem, Cosmog, Cresselia, Darmanitan-Zen, Deoxys, Duosion, Elgyem, Espurr, Exeggcute, Exeggutor, Gothita, Gothitelle, Gothorita, Grumpig, Hoopa, Inkay, Jynx, Latias, Latios, Lugia, Lunatone, Malamar, Medicham, Meditite, Meowstic, Metagross, Metang, Mewtwo, Mime Jr., Necrozma, Oranguru, Oricorio-Pa'u, Raichu-Alola, Reuniclus, Silvally-Psychic, Slowbro, Slowking, Slowpoke, Smoochum, Solgaleo, Solosis, Solrock, Spoink, Swoobat, Unown, Wobbuffet, Woobat, Wynaut
The Japanese name for Dazzling Gleam is Magical Shine, so I think it's fair to rule out those that are based on machinery (Beldum), extraterrestrials or space objects (Deoxys/Solrock/Lunatone), or biological processes (Solosis line). While some of them may seem unnatural, they are all inspired by phenomena that has been observed or theorized in scientific field (not a scientist but I am 90% sure most scientists do not consider magic in their reasoning.) I will leave Cresselia and Necrozma in and explain that later. Mewtwo is included here because it is a man-made Pokemon and while Team Rocket R&D are quite skilled, I would not call them magical.
Arceus-Psychic, Beheeyem, Beldum, Bronzong, Bronzor, Bruxish, Cosmoem, Cosmog, Cresselia, Darmanitan-Zen, Deoxys, Duosion, Elgyem, Espurr, Exeggcute, Exeggutor, Gothita, Gothitelle, Gothorita, Grumpig, Hoopa, Inkay, Jynx, Latias, Latios, Lugia, Lunatone, Malamar, Medicham, Meditite, Meowstic, Metagross, Metang, Mewtwo, Mime Jr., Necrozma, Oranguru, Oricorio-Pa'u, Raichu-Alola, Reuniclus, Silvally-Psychic, Slowbro, Slowking, Slowpoke, Smoochum, Solgaleo, Solosis, Solrock, Spoink, Swoobat, Unown, Wobbuffet, Woobat, Wynaut
Some of these can be explained right off the bat:
Bruxish draws inspiration from groupers and reef triggerfish. While both can be very colorful to the eye, nothing about them can really be considered magical and neither are bioluminescent under normal circumstances. (Bruxish is a design that, to me, is in the vein of Durant or Stantler in that it's very literal about what animal it's based off of) Similar logic can be explained for
Woobat and
Swoobat, and the
Exeggcute line as bats and eggs are hardly candidates for light generation.
Mime Jr. is probably cursed with the shallow movepool of a baby Pokemon, seeing as its evolution gets the move and STAB on it anyways.
Lugia, while a sea god of some capability, is not considered a light generator or a particularly "shiny" Pokemon (it leaves that to based fire turkey Ho-Oh). The
Slowpoke line could be considered as too "dumb" to learn it, where
Slowking represents the upper limit of the species intelligence and is analogous to real humans, who can't really use magic.
Solgaleo might be an oversight as its counterpart
Lunala actually does get Dazzling Gleam, or it could represent the connection that Fairy Pokemon have to the moon (many Fairy-types get Moonlight and Moonblast is one of the strongest Fairy-type moves). Solgaleo substitutes that with a myriad of Fire-type moves that Lunala can't get.
Meditite and
Medicham are based off of meditating warriors; while their training is impressive it isn't beyond human capability and thus Dazzling Gleam shouldn't be an obvious consideration. (plus a hermit in a cave who lives on berries is not gonna be shiny looking) While not a great reason,
Hoopa misses out perhaps to emphasize its vulnerability to Dark-types (though it does get Focus Blast, so at that point I got nothing).
The Inexplicables:
Espurr and
Meowstic have access to other Fairy-type moves such as Draining Kiss, and other cat/mammal Pokemon such as Espeon and Cinccino have access to the move, so why not them? Humanoid Pokemon including Meloetta and Alakazam (and fucking Hypno) get access to this, so there's no reason
the Smoochum line,
Oranguru, and
Gothita shouldn't get it (Gothitelle is even based off astral projection, which is pretty darn close to magic for me).
Inkay and
Malamar are based off of squid, which are notorious for putting on light shows, especially when mating (if Starmie gets it for a gem, these two definitely deserve it). Talking of gems,
Spoink and
Grumpig have some pretty sizeable pearls that could refract light (they can also learn Signal Beam, Power Gem and Flash). And talking of refraction,
Necrozma is basically all about shining light (its fucking signature move is Prismatic Laser). It does get a slight pass due to its movepool being very weirdly limited in other ways.
Cresselia, though, is intrinsically linked with the moon (Fairy connection, it even gets Moonblast). Lunala (another lunar mon) gets this so why not the original crescent? (fuck right off lunatone)
So in conclusion, there are reasons for some of the Psychic type getting it because it's quite a varied type when it comes to inspiration. But Game Freak's hands of judgment strike some Gleam-less Pokemon harder than others.