And what is that core? Reading minds, throwing things with their mind, and precognition can be spells. Having an energy blade means the fighting style is primarily Melee. And Jedi have supreme control over their bodies, so pretty much a Monk. In fact, exactly a Monk, adding in a blade and some spells. The Monk already does everything a Jedi does, just without the energy blade and spells. Why build a whole new class when there’s already a class available that does what you want, and a subclass system that accommodates adding in new features to that class?...
The 'jedi' is an easy access reference point that people can understand, but - in my vision of how the psychic warrior should work - it is not a complete picture. I suggested 5 builds for a psychic warrior, all built around a base class:
The base class would be medium armor, all martial weapons, and a small suite of psi powers (much less than the psion) from which to choose - in my mind they'd work similarly to Warlock invocations rather than spells. Then, they would have their own 'Orders/Focuses' that grant the tweak that individualizes their methods. However, from level 1, they'd be attacking foes with a combination of the physical and mental. For example, they might have an ability that allows them to forgo dealing + Str or Dex damage on a melee hit to instead inflict a condition (slow foes movement, make them see phantasms, etc...) The subclasses could be:
Soul Knife - a melee defender that makes psychic weapons and deals damage. Their equivalent in the non-psychic world would be an eldritch knight two-handed weapon fighter. They hit pretty hard, and are durable tanks, but have the fewest tricks of the psychic warriors. They still have some tricks, but like an Eldritch Knight they always wish they had more. The majority of their psychic abilities would be dropped into augmenting their soul blades for particular purposes.
Immortal - This would be similar to a soul knife, but rather than devote their psi to weapons, they devote the majority of their psi to protection. They are hard to take down, and they make it hard to take down their allies. Their equivalent out of psi would be a sword and board paladin, but the mechanics and feel would be very different. However, if you put one at the vanguard with a couple beater melee classes you'd really feel their presence holding their allies up while still being effective on the field themselves - just not as effective as the soul knife in dealing damage.
Disciple - This would be a lower damage build than the high damage soul knife or solid damage immortal, but still a melee build. Their shtick would be what we saw from Vader when he fought Luke in Cloud City - He attacks with weapons and augments those attacks with telekinetic (and other environment impacting) abilities. They make it hard for opponents to function due to the chaos they create around themselves. I'd equate them to a melee cleric most closely, but it really is something we do not have in 5E. This is the psychic warrior you want when you face an army and want to have one man make a difference.
Dominator - Similar to the Disciple, this build is a melee build that gets into the thick of things but is not as durable as the Soul Knife or Immortal. Instead, they rely upon tricks of the mind to win the day. They mix in mind control, illusion, and inflicting some conditions - disrupting the enemy rather than the enemy's environment. They don't impact as wide of an enemy force as the Disciple, but their impacts are a bit more intense.
Mindhunter - This is a true psychic hunter with powers that break an individual foe. While the Dominator blankets an army with charm or paralysis, the Mindhunter grabs the mind of an individual foe and tears into it. They inflict more powerful conditions, but only to single targets... and they make permanent marks when they do it. They don't just dominate you - they leave a piece of their mind in yours, allowing them to reestablish control at a later date. They take memories out of your mind. They implant the frightened condition when they are present - until the condition is removed. They give you phobias that last until removed. They'll dominate a foe and hold that foes mind for as long as they can concentrate. When their blade pierces your flesh, you enter a realm of nightmares that may be with you for the rest of your life.
Could I create each of those subclasses within existing classes? Yeah. I could. I could also make all clerics into fighter subclasses. It just wouldn't be the BEST way to build them.
I want a psion with subclasses, and a psychic warrior with sublasses ... and I don't mind seeing a few new subclasses for other classes that have psychic focuses, but they should only be situations in which the psychic abilities are the nuance, not the focus, of the build.