That is not unreasonable, but why the hell should that class be the sorcerer or even in core? Why can't I have a dragon-blooded fighter or a dragon-blooded rogue?
Look at how 3e did it. There were two 'dragon' base classes, neither of which was sorcerer. There were also feats that let you adapt several other classes to be more draconic.
The whole draconic bloodline thing is actually a complete and utter betrayal of the original concept. It's not 'iconic' in the slightest.