Neither class should be a subclass of the other. Because both classes exist due to narrative reasons and not mechanical ones.
The narrative of the Wizard is that they can learn to tap into the arcane weave to generate magical effects. The narrative of the Sorcerer is that they have a magical wellspring already within them (based upon their ancestry and bloodline). Neither of those two stories can or should fall under the other. They should remain separate.
What SHOULD happen (in my opinion) is that Sorcerers should no longer be said to use Arcane magic (nor the Warlock for that matter). Arcane magic comes from being able to tap into the weave of magical power that permeates the cosmos and across the world via the Astral and Ethereal planes. To do so, you need to learn how to do it. Wizards do. Bards do. Artificers do. They all use (dare I say) "science" and "experiment" to figure out how to access this weave-- mystical words, motions, sounds, harmonies, objects etc. that can let a person tap into the weave of arcane magic.
Sorcerers don't do that. There's no learning involved. They aren't tapping into anything. They just have instead this "wellspring" of magic within them. But if they aren't accessing the weave, why would we call this magic Arcane? We shouldn't. They aren't the same thing. The magic of Sorcerers should be of a different type of magic than what Wizards, Bards, and Artificers use. For my money, all the classes that just have magic within them here on the Prime plane... the Sorcerer, the Psion, the Monk, the Druid, the Barbarian, the Ranger... they are each one of the lucky ones who were born into the Prime plane being able to access the power and energy of the world itself (including within themselves, as they are a part of the world.) For my money... they are all wielder of Primal magic. Magic of the Prime. Half of them draw their magic from the earth and nature (Druid, Barbarian, Ranger)... the others draw their magic that bubbles up from within themselves (the Sorcerer, Psion, and Monk).
That being said... if folks felt it was necessary to separate the magic drawn from the world itself from the magical spark found within a person (in other words, the idea that "sentient creatures" are not just a part of the world and thus has magic within them just like the world does... but rather that they are special and separate from it and thus their magic is too)... then you could keep Primal magic for the D, B & R and create a new category of magic (say Innate or Mystical or Psionic) for the Sorcerer, Psion, and Monk.
That of course then leaves Cleric, Paladins, and Warlocks... all of whom form a connection to a god, a creature, or a tenet from the Outer Planes via worship, bargaining, or having just such a conviction in something that a path opens before them. These three classes are all granted magical ability from an outside force. We can keep calling it Divine power, but you could also say it is Planar power.
If you did this... actually made a more definitive narrative around these (dare I say) "power sources" and actually cleaned up the exceedingly wishy-washy phrase "Arcane Magic" into something more definitive... you would absolutely have a better chance at separating the Sorcerer and the Wizard from each other once and for all. (And would finally hopefully cut back on the number of people who think the Sorcerer, Wizard, and Warlock are all interchangeable and should be merged or subclasses under or into each other.)
