I have never understood the "Sorcerer has no identity" thing; they've always stood out opposed to wizards for their inborn magic and the bloodlines introduced in 5e only deepened that.
Okay, I'm not going to touch the class identity war thing, but....

SORCERER

IS

NOT

BLOODLINES

!!!!!! Dragon sorcerer was bloodlines, but wild magic, storm sorcery, clockwork, aberrant mind, divine soul, moon magic, and shadow magic were NEVER bloodlines.
Pathfinder was the one that went all in with sorcerer=bloodlines. D&D has not done so. There's the option that SOME sorcerers claim decent from dragons, but that was never baked in, only a suggestion, even back when sorcerer first debuted in 3e. Other options included being mentored by a dragon or bathing in dragon blood. Same thing in 4e (which even had an Elementalist name later in the edition) and 5e (more like mutants exposed to energy to make you sensitive to its manipulation).
The D&D sorcerer is defined by specializing in tapping into certain types of magical planes for an elemental mage archetype. So you end up with classic elemental magic of fire, lightning, ice, etc (dragon, storm), positive energy (divine soul), necrotic energy (shadow), far realm for mind magic (aberrant mind), chaotic planes (wild) and lawful (clockwork). Magic in dragonlance comes from the moons instead of other planes, so we have a subclass specifically made to align itself to the dragonlance moons.
Take a look at all the cool crystal magic items made specifically for sorcerer in Tasha's Cauldron of Everything. They're all planar-based. You get one from the elemental planes, from the four alignment planes, from the far realm, from feywild and shadowfell. They enhance the ties for being a "fire elemntalist" or "chaos magic user" type stuff.
You want bloodline magic? That's elf, tiefling, gnome, and more. Actual species that start with magic spells as part of their package. That's different from being a sorcerer.