A huge barrier for many people is they have no understanding of what programming will enable, what it entails, and its varying difficulty levels.

I think there are so many "pre-med" college freshmen because everyone understands the role of a doctor. If programming were more tangible and widely understood, there would be far more people doing it (and luckily this is rapidly happening).

Maybe this is also a good way to teach your daughter college-level abstract algebra.