1) There is a basic, fundamental difference between a Core class and a Non-Core (or what Wikipedia calls "alternative" class). I think we all get this. Core classes have a lot more momentum and compelling reason to include in an edition. A Non-Core class does not have the same level of incentive to include it.
2) Psion/Psionicist is a Non-Core class.
3) There is more motivation to include a Non-Core class which has been in more prior editions, or which was featured as a more prominent Non-Core class in a prior edition, than there is for a one-time Non-Core class from one prior edition.
4) However, just being in many prior editions is still not, in itself, enough reason to include it now without something more.
This is the controversial question I will address with this post.
Operating off these basic concepts, which I think are all correct (though the last one is in question), we can compare where the Psion/Psionicist class really falls along with other Non-Core classes.
There are a ton of Non-Core classes that will probably never be heard from again (and some which were subsumed by other classes or sub-classes or prestige classes or kits or whatever).
For example, 1e had Bushi, Kensai, Ninja, Samurai, Shukenja, Sohei,
Wu Jen, and Yakuza, Mystic, Witch, Thief-Acrobat, Cavelier, Knight of the Crown, Knight of the Sword and Knight of the Rose, Wizards of High Sorcery, Tinker, etc.. And I am not including Dragon Magazine. I see you Jester!
2e had all of these Non-Core classes: Guilder, Manteis, Chronomancer, Temporal Champion, Temporal Raider, Incantatrix, Defiler, Elemental Cleric, Gladiator, Para-elemental Cleric, Templar, Trader. Dragon, Avangion, Anchorite, Arcanist, Avenger, Gypsy, Handler, Tinker, Commoner, Knight of Solamnia, Mariner, Wizard of High Sorcery, Holy Order of the Stars, Crusader, Mystic, Shaman, Ascetic, Pious Knight, Apothecary, Appraiser, Blacksmith, Cartographer, Engineer, Guide, Healer, Historian, Scribe, Seer, Solitary Shaman, Spiritualist, Tribal Shaman, Alchemist, Geometer, Shadow Mage, Song Wizard, Dimensionalist, Force Mage, Mentalist, Ninja (Spy/Killer), etc.. And that list included Psionicist.
And that's NOT INCLUDING THE KIT CLASSES! You can triple that list when you include those! I see you, Jester class (again). I see you, Halfling Whistler. I see you, Treetender, Anatomist, Consort, Mountain Man, and Gaucho!
As you can see, being a member of that list is not, in itself, a compelling reason to be in 5e.
OK so let's look at 3e. We have such lovely Non-Core classes as Archivist, Beguiler, Binder, Crusader, Dragon Shaman, Dragonfire Adept, Dread Necormancer, Duskblade, Factotum, Favored Soul, Healer, Hexblade, Incarnate, Knight, Marshal, Ninja, Samurai, Scout, Shaman, Shadowcaster, Shugenja, Sohei, Soulborn, Spellthief, Spirit Shaman, Swashbuckler, Swordsage, Totemist, Truenamer, Warblade, Warmage, Wu Jen, Mariner, Master, Mystic, Nightstalker, Noble, Magewright, Urban Adept, Samurai, Shaman, etc..
Oh and let's not forget the specific Psionic classes of (drum roll please) Psychic Rogue, Psychic Warrior, Divine Mind, and Wilder, among others. Hrm, where have I heard of those concepts recently?
I've left out a bunch more, but you get the drift. Being on this list isn't, in itself, a compelling reason to exist in 5e.
And we're seeing some patterns of classes which 1) appeared in many editions but which 2) do not exist in 5e, and 3) which have few people clamoring for them to exist now in 5e.
Where are all the people claiming "Oh but Shaman has been in every edition of D&D so we absolutely must have it now in 5e"? Where are all you Wu-Jen and Ninja fans at? Where are the Witch fans? I seem to recall there was a Jester class for 3e too, so where are all you Jester fans?
4e didn't get far, but they still had Ardent, Avenger, Invoker, Runepriest, Seeker, Shaman, Swordmage, Warden, Spellcarred, etc.. And there it is again, Shaman. We've had a Shaman in every edition - I see no "OMG it's long established tradition to have a Shaman we must must must include it!" threads popping up. Have I missed it?
So here's the bottom line: being in many prior editions is still not, in itself, enough of a reason to include that class in 5e. It helps to have been in many editions. It adds something to the argument that something should be in 5e. But it's not sufficient, in itself, to say it must be included. Because if it were, you'd see the same sort of passion concerning a Shaman class. Or a Witch class. Or a Wu-Jen class. Or Ninja class. Or even, God forbid, a Jester class. All classes which have appeared in many editions, which are not in 5e, and which don't seem to have much push to be included in 5e now.
So you're going to have to do better than "It's been in three editions" for a Non-core class.