I am willing to bet good money that teaching pure mathematics like group theory, abstract algebra, or stuff like big Oh and combinatronics will do our kids a lot more good and advance them far more than calculus or geometry as taught in schools will.
I have the same experience as you did, in that studying by myself abstract algebra accelerated my learning and reasoning skills.
I think differential equations was where the switch from "I'm good at math" to "I think I want to actually know more of this" happened. I changed my major from engineering to physics. But agreed, abstract algebra was another big change and after that I took every class my university would let me and the chair of the department even made some new ones for me and some others.
I don't think this experience is uncommon (among people who get to these levels). Which is why it is really sad. Especially given how linear algebra and abstract algebra are in a lot of ways easier than calculus. I also think they should be taught earlier purely due to the fact that they teach abstraction and reasoning.
I have the same experience as you did, in that studying by myself abstract algebra accelerated my learning and reasoning skills.