What is this "mandatory Wizard training" you speak of?
All 3.x wizards needed to be trained in Knowledge arcana and spellcraft in order to work at all, sorcerers and warlocks didn't but could do so if they wanted, this was good because the academic flavor was only a possibility, but your sorcerer or warlock could come from anywhere and be developped as anything, no mandatory wizard college or studying on the dark tower. 4e stuck all arcane classes with mandatory Arcana training, this wasn't so bad because like I said it wasn't only academic knowledge, but also covered some minor forms of spellcasting, and it was still completely possible to avoid it by building as an hybrid. 5e so far has gone beyond mandatory knowledge on how magic works (Esoteric Knowledge) it also assumes every sorcerer and warlock has actually trained on wizard college or studied in the dark tower
Really? So, Basic D&D didn't have only 3 or 4 core classes that were relatively bland (Hello, I'm a fighter...I hit things). 1st edition didn't have a small core of classes? Were those D&D?
OD&D was three classes.
AD&D and BECMI was four. 2e was, mostly, as well.
4e was four "types" instead of four classes.
I'd say a majority of D&D versions used this concept of distilling all classes down to three or four classifications, and then spread out variants from there.
Why would a Psion need a different hit point, ability/feat, number of spell/psionic per level, and attack bonus than a mage or a sorcerer (I think armor will be listed for each sub-class btw, just like it was done for Cleric/Druid in earlier editions)? Similarly, why would a Paladin need a different progression on those factors from a fighter? Sub-classes worked just fine in older editions of D&D in this same manner.
I really think you're getting too caught up in titles, and assuming way to much about how things will function, all from a short tweet. You can have massive variation in how each sub-class operates, despite the primary class title. It's mostly a "how do we organize the book, balance things, and use a bit of short-hand to save space" type thing.
That's not entirely accurate. 2e also had sub-classes. Ranger and Paladin were sub-classes of Fighter. Druid was a sub-class of Cleric and Specialist Wizard's were sub-classes of Magic Users.
It was 3e that did away with the notion of sub-classes.
Mechanically, what is different between a 3e Wizard and a Sorcerer? They are virtually identical. The only real difference is in the memorization rules. They use identical spell lists and cast exactly the same way. Psionics have been done both as Vancian casting and spell points at various points in time in the game. These classes really aren't that different IMO.
This is a misconception, the original basic booklets only had three classes, but they quickly grow out beyond that number, by the very first supplement there were more than 6. Then when Basic itself came out it had seven classes, and first edition had eleven. So no, no edition of d&d has only had 4 classes. (Second edition had 4 CLASS GROUPS not Classes)
Sublcasses in 1st edition were pretty tame, they didn't limit anything, their main use was to recycle saving throw and to-hit charts which if I have to guess were cumbersome to print over and over, so it made sense to have only five of them. (And because they were on the DMG). Likewise second edition didn't have subclasses, just class groups, those shared only saving throw, Thaco and proficiency progressions, but each class had it's own features and xp table. and it is a big lie that paladins and rangers were subclasses of fighter, they all were full classes under the WARRIOR group, just like thieves and bards were under the ROUGE group, or Druids, clerics and specialty priests under the PRIEST group
3rd edition stopped using subclasses, because they had stopped meaning anything, the simplified to hit and saving throw progressions coupled with the universal xp chart made it possible for each class to have those numbers printed on their table, suddenly the only function they had was to stop similar classes from multiclassing with each other, so doing away with them was a good measure.
This isn't about being caught up with titles, but also comes from more pragmatic reasons, (like increased complexity, reduced customizability, hidnered flavor, reduced power -sorcerers and warlocks will be very weak if stuck on the same feat schedule as wizards-). It would be simpler if they just made sorcerers and warlocks their own classes with a feat progression tailored to cover their weaknesses (which the wizards don't share), features tailored to their flavor and the just use some keywords, or put a disclaimer saying that they can use all wizard magic items that work for them.
(And again 3.0 wizards and sorcerers weren't the same, not quite close, they didn't even played the same, beyond they casting the same spells -and this is a stretch, because sorcerers normally refrained from highly situational spells unless they focussed all other resources into mundane utility-, stop repeating it like some kind of mantra, they weren't even the same archetype)