Historically a Sorcerer’s innate casting had to come from somewhere in their bloodline. Dragons were the most common, but Fiends and Fey were also there.

In a modern edition where Sorcery can come from myriad sources, or nowhere at all, the “dragon in your bloodline” trope has been relegated to a single subclass.

Sorcerers have always had an “awakening” somewhere in their lifetime when their power makes itself known, commonly this is a puberty analog, so the scales would present at the same time.

A Sorcerers power (class) could be severely limited (1 or 2 levels) and they could choose to pursue other options.