Go back to the flavor text (emphasis mine)...
[SECTION]RAW MAGIC
Sorcerers carry a magical birthright conferred upon them by an exotic bloodline, some otherworldly influence, or exposure to unknown cosmic forces. One can’t study sorcery as one learns a language (1), any more than one can learn to live a legendary life. No one chooses sorcery; the power chooses the sorcerer (2).
Magic is a part of every sorcerer, suffusing body, mind, and spirit with a latent power that waits to be tapped. Some sorcerers wield magic that springs from an ancient bloodline infused with the magic of dragons. Others carry a raw, uncontrolled magic within them, a chaotic storm that manifests in unexpected ways. The appearance of sorcerous powers is wildly unpredictable. Some draconic bloodlines produce exactly one sorcerer in every generation, but in other lines of descent every individual is a sorcerer. Most of the time, the talents of sorcery appear as apparent flukes. Some sorcerers can’t name the origin of their power, while others trace it to strange events in their own lives. The touch of a demon, the blessing of a dryad at a baby’s birth, or a taste of the water from a mysterious spring might spark the gift of sorcery. So too might the gift of a deity of magic, exposure to the elemental forces of the Inner Planes or the maddening chaos of Limbo, or a glimpse into the inner workings of reality. (3)
Sorcerers have no use for the spellbooks and ancient tomes of magic lore that wizards rely on, nor do they rely on a patron to grant their spells as warlocks do. By learning to harness and channel their own inborn magic, they can discover new and staggering ways to unleash that power. (4)
UNEXPLAINED POWERS
Sorcerers are rare in the world, and it’s unusual to find a sorcerer who is not involved in the adventuring life in some way. People with magical power seething in their veins soon discover that the power doesn’t like to stay quiet. A sorcerer’s magic wants to be wielded, and it has a tendency to spill out in unpredictable ways if it isn’t called on. (5)
Sorcerers often have obscure or quixotic motivations driving them to adventure. Some seek a greater understanding of the magical force that infuses them, or the answer to the mystery of its origin. Others hope to find a way to get rid of it, or to unleash its full potential. Whatever their goals, sorcerers are every bit asuseful to an adventuring party as wizards, making up for a comparative lack of breadth in their magical knowledge with enormous flexibility in using the spells they know. (6)[/SECTION]
(1) suggests that sorcerers don't use the "language" of magic (spells) as other spellcasters do. For example, PHB p. 201 says "In casting a spell, a character carefully plucks at the invisible strands of raw magic suffusing the world, pins them in place in a particular pattern, sets them vibrating in a specific way, and then releases them to unleash the desired effect — in most cases, all in the span of seconds." But sorcery isn't pre-defined, it isn't a pattern language, it isn't set in a specific way. Yet the PHB sorcerer relies on spells readily recognizable to wizards. Easy on players – perhaps (more on that below) – but ultimately not matching the flavor text.
(2) suggests that magic, at least the kind sorcerers are tapped into has a will or semi-sentience of its own. What if sorcery were like riding/taming a stallion, using mechanics akin to a battle of wills with a sentient magic item? What does it mean for magic to choose you; do you always detect as magic, do others always recognize you as a spellcaster, or what? Are there unwilling sorcerers? Some of this is worldbuilding, but it could easily translate into mechanics that actually follow up on the promise of this flavor. Again, the mechanics fail.
(3) draws attention to the fact that "most sorcerers are not bloodline based at all! They're instead defined by strange events and involve significant mystery. If a sorcerer's origin is a mystery, should the player be pinning that down OOC? Isn't that a bit jarring narratively? Maybe what matters more than a sorcerer's past is their present ("how do you respond to magic choosing you? embrace it? see it as a curse?") or their future ("what do you seek to accomplish with your gift? pass it on? return it to its source? find the truth of your power's origin?").
(4) makes me wonder: Does Metamagic qualify as "discovering new and staggering ways to unleash that power"? Definitely Twinned Spell is powerful, but I'd argue there's no real sense of discovery on the player's side. Metamagic becomes rote eventually... "Oh, it's longer-reaching. Oh, there's 2 lightning bolts. Oh, you cast it subtly." Something is missing. Instead imagine a sorcerer mixing gust of wind and hypnotic pattern to blow a scintillating cloud into the castle window - a spell combo! Or imagine a sorcerer empowering a fire bolt so it twists around corners or appears as a roaring dragon's head of flame! Or even consider a sorcerer circumventing the usual spell system entirely to do things no bard, warlock, or wizard could dream of – like dropping a gravity well among enemies, slamming them together like those bombs from Guardians of the Galaxy!
(5) Magic wants to be wielded. Unused magic spills out in unpredictable ways. It seethes in a sorcerer's veins. What a powerful statement! If this flavor text were actually reflected in the design, what would it look like? Maybe instead of spell slots, a sorcerer builds up wild surge charges, so the more magic/spells cast, the greater risk of spending a round not casting a spell? Maybe losing concentration is particularly dangerous for a sorcerer? Maybe during a long rest, unused spell slots increase the chance of "strangeness" afflicting the sorcerer? So many opportunities to interpret this powerful flavor text, and yet sorcerer's design misses all of them.
(6) "Narrow focus, but enormous flexibility." Sorcerers aren't swiss army knives, with a utility spell for every occasion like a wizard. A sorcerer is a hatchet with uses limited only by the player's creativity (or perhaps necessity). A sorcerer has a tight theme but can adapt magic within that theme to a wide array of effects; a sorcerer might only know "water magic" but he knows *every* way to use water! And he can change it up on the fly! Instead, the PHB gives us the same old spell system without significant variation. Ice storm is ice storm is ice storm; if you want to use it to freeze a reservoir, well, you're firmly in DM judgment call territory just like any other spellcaster.
The Sorcerer flavor text is describing a class concept that does not actually appear in the PHB, but it's a class concept I recognize from fiction (e.g. A Wizard of Earthsea) & one I'd love to see actually implemented in D&D.