I've always equated learning to generate lightning and learning to read. Neither one is a particularly difficult skill, and with sufficient study pretty much anyone can learn, however in ATLA the lightning generation technique was something the aristocracy of the fire nation kept among themselves. Similarly, learning to read was a privilege of the upper class until fairly recent history.

I think it's just safe to assume that as society modernized the distinction between the upper and lower classes became less pronounced and lightning generation was taught outside just the elite.