TwoSix
Master of the One True Way
Personally, I'd lean into this even harder. A sorcerer isn't a spellcaster at all; they're a magical being. As they level, they get more and stronger special abilities based around their magical theme. The sorcerer "class" has almost nothing, other than granting saves/skills/hit die/ASIs.We could move Sorcerers closer to having "spell like abilities".
Ie, a sorcerer doesn't learn spells and spend spell slots. A sorcerer learns spell like abilities, and each time they use them in a day they have a chance to not be able to do so again.
Second, to distinguish a sorcerer from a wizard, what if we added riders to each spell like ability. Like, when a sorcerer gains the fireball spell like ability it comes with a package of other abilities. This is somewhat similar to the "domain" idea, but maybe at a finer grain level.
An easy example would be that every time you learn a fire spell like ability, you get a +1 bonus to damage on fire spells (including cantrips).
To make it a bit less generic, imagine if the Sorcerer class had a set of Domains. Each Domain was associated with a set of spells. As you get more spells in a Domain, you get extra passive abilities.
Domain of Fire might grant an increasing amount of bonus damage with fire spells. If you have N spells, it roughly adds +1dN to your fire spell damage. It will also eventually grant fire resistance (and maybe immunity), plus maybe cold resistance.
If the sorcerer wants higher level domain abilities, the sorcerer is encouraged to pick more fire spells.
Possibly a given spell can belong to more than one domain. When you pick a spell like ability (aka spell), you pick which domain you are going to boost. This lets us come out with new Domains that overlap existing ones without automatic power creep.
I could also get behind a sorcerer picking one, and only one, domain, sort of like the 3.5 PrC Divine Crusader. A "domain" has exactly one spell of each level, organized around a theme (Fire, Ice, Fear, Nature, etc.). The sorcerer casts these with sorcery points. The sorcerer subclass is what grants the theme of the character (draconic, fey, celestial, etc.), and generally gives the combat scaling, utility, and ribbon powers. The domain and subclass combined gives the overall concept, like a fire domain draconic sorcerer.