I don't see what's so restrictive about bloodlines. Just because bloodlines exist in the world doesn't mean they have to be at all common. It's not like none of the other classes put restrictions on your setting either. The Cleric, and by proxy all the other divine casters, require that there be gods in the world that grant powers to mortals that follow them. The Warlock similarly requires that there be powerful beings that grant boons and powers in exchange for...actually, what do they get in exchange for granting a warlock their powers? I guess I never really understood that.

They're also extremely easy to re-fluff. For example, instead of having "the blood of a dragon", you could say that they were corrupted by some artifact, which gave them magical powers. Or maybe becoming a sorcerer is something you learn, and the various powers you get are just more things that a sorcerer learns how to do as they progress. If you don't like dragons, you could swap out the fluff for, say, elementalist fluff. Instead of dragon scales, your skin hardens like rock. Instead of breathing fire, you shoot a jet of flame from your eyes. And so on.