I would made an in depth point by point post, but AgentPaper said most of what I was going to say just as good if not better than I could have said it.

I want to reiterate how significant the powers of the presented bloodline are. I am honestly a little worried that if bloodlines are all as powerful as the draconic bloodline, than bloodline might overshadow the sorcerers spell casting abilities. Their activated powers are every bit as good as spells, and the passive benefits turn them into a really good melee warrior. It's a very significant part of a character.

I also want to reiterate that fighter and rogue are pretty much the only classes whose abilities are setting independent, and even then they assume a high fantasy setting at that. D&D has shapeshifting tree huggers and martial artists who can heal their wounds and kill someone with a strike. Dragon Sorcerers are not a stretch.

As far as racial elements in a class. You have to understand that in this case, game mechanics are king. The mechanics of a game always take priority over fluff, and this is especially true for D&D, which is essentially a small group war game.(not saying you have to play it as a war game, but it's a chainmail spin off whether anyone likes it or not). The single most influential part of your characters mechanics is your class, your race and feats are very minor compared to your class. So if you want a character with a strong draconic magic theme to them that is represented by mechanics, it needs to be a class. That's your only option. Making a series of draconic magic feats will just feel like a feat tax for people who want them, and ignored by everyone else, and balancing a draconic magic race will be a nightmare. If a dragon sorcerer is going to exist, it has to be a class.