The sorcerer flavor text emphasizes supernatural bloodlines, raw magic, cosmic exposure to magical radiation, and the like. A sorcerer is described as being a spellcaster that suffused with magic so that it comes naturally: they are magic. This isn't really at all how a psion is described. Their powers are innate to the extent that the mind is part of the self.
Psions are described as spellcasters who harness the power of the mind through a form of mental discipline. It's not necessarily either a narrative of "born this way" (as per the sorcerer) or "learned this way" (as per the wizard). What matters is that the power comes from what the mind, and psionics is concerned about what the mind can achieve. The wizard may ask, "What are the bounds of magic?" but the psion will likely ask, "What are the bounds of my mind?"
Honestly, I think you are splitting hairs. The examples you mention above...which are essentially direct quotes from the PHB...to me sound like they could neatly cover psionics. I get Big Bucky's point and am sympathetic to it: both sorcerers and psionicists (intentionally not using the word Psion here because I think maybe it carries baggage/connotations/expectations) have innate power. You either have it, or you don't. So, yeah, in many ways the Sorcerer could make a good chassis for a psionicist.
The flip side is that oodles of Sorcerer spells don't really fit the (or my) image of a psionicist, and there's not real mechanism or precedent in 5e for removing spells from a base class spell list.
Another downside is that Sorcerers are very clearly...it is stated repeatedly...about magic. And even if psionics officially are considered magic (for the purposes of detecting, dispelling, etc.) to me they feel like...something else. Certainly if Divine and Arcane magic are siblings, or half-siblings, psionics are a distant cousin, several times removed. And probably the result of a hushed-up affair with an exotic dancer.
And, finally, I've always been in the camp that Sorcerers are really so close to Wizards...Vancian casting, spell slots, etc. etc. etc....that why even bother including them? So I'm all for a totally different mechanic. Not because a psionicist couldn't simply be a refluffed sorcerer...it could...but because it would be fun to use a completely different set of mechanics.
Is there any possibility that's really where you're coming from, too? If so, I don't think it's necessary to try to argue why a different concept can't re-use mechanics and must have distinct mechanics. It's simpler, and irrefutable, to say, "I'm tired of the standard spell mechanics and I would have more fun playing something more distinctive."