What is the sorcerer's reason for existence? Does it have enough traction to continue as a class?
When introduced in 3rd edition, its only distinction from the wizard was limited spells known and more spell slots. The class was a reaction to Vancian spell preparation, but didn't introduce any new story elements to support the mechanical change.
The very first paragraph of the description introduces where they are different from a narrative perspective. They are the raw talents, the ones who control magic innately instead of through study. And it even brings in that some claim draconic bloodlines. We have a story description.
(If you are conflating "story elements" and "specific setting lore elements" then that
shouldn't be in the core books.)
And really, a native talent arcanist is a common archetype in novels, shows and movies. It is fulfilling the primary duty of a class - allow players to create characters to fulfill archetypes and genre tropes. Mechanics are just how, and never by themselves justify a class. This is the "why", and it's a good one considering how common those archetypes are.
Over time, and through into 5th edition, designers leaned into the "ancestry" theme, proposing sorcerer variants and subclasses that granted new spells or magical powers so the PC could be more like a dragon/demon/angel/aberration/etc.
Not wrong, but incomplete. Less than half the subclasses focus on an ancestry, with the majority mentioning an ancestry or "growing up near a source of X" or just "born with them" as one possible source while also listing other sources that are not ancestry themed. I was surprised when I first realized this myself.
So the PC got some story hooks, but they always came from the customization and not the base class. In 5th edition the design also introduced sorcery points and metamagic for sorcerers--but as with the 3rd edition innovation, this feature is a meta-gaming rule innovation intended to create contrast with wizards, with minimal story or flavor to back it up.
The flavor that sorcerers are the masters of their magic, so they know fewer spells but can do more things with them than a wizard?
Sorry, that's been well established, this is also wrong.
On the other side of the fence, the wizard also got new magical powers through "specialization". Initially this provided more spell slots and a boost to learning spells in one of the "academic" schools, but wizard specializations now have much wider variety than the 8 schools, and also grant innate magical powers to the PC.
Yes, classes get subclasses with features. This is a truism.
Consider a wizard and a feyblooded sorcerer, both specialized in illusions.
No, I won't. Because you are putting restrictions on the feyblood in order to have it match a particular wizard subclass. And you're not even doing with an official subclass, so I have no idea or care how much an official subclass is to a wizard subclass.
The two PCs have different innate powers via their subclasses, but in 5th edition they both prepare spells, cast with spell slots, can modify their spells (the wizard needs more time and does it later), get some extra spell slots (arcane recovery vs sorcery points)... in short they are functionally very similar.
Um, no, they don't both prepare spells. The sorcerer has spells known. Quite a different mechanic.
Yes, they use spell slots, just like clerics and rangers and everything that uses spells, just like we use a d20+modifiers >= to a target - it's a universal mechanic for ease of understanding.
And saying that because they use a universal mechanic of spellcasting they are similar is saying that the druid and the wizard are similar. It's too far to even be a stretch, it's irrelevant.
Frankly, my own feeling is that the sorcerer has outlived its usefulness as a base class.
First, what you said could equally be that the wizard has outlived it's usefulness as a base class.
Second, every point you've brought up has been factually incorrect, incomplete, or irrelevant.
Come back with a solid foundation and we can talk about your ideas. But your understanding of the sorcerer is profoundly flawed. I'm not even a fan of the current implementation of the sorcerer but I feel compelled to set right the facts instead of this narrative.