> Tragically, many students disengage before this can happen because of sheer boredom and the tedium of endless math drills

It's tragic and all, but were there attempts to teach non-preselected children/adolescents interesting stuff first? What are the results?

I don't know.

There is a certain amount of drudgery that unavoidable in learning mathematics, IMHO. Moreover, looking at the math textbooks of my niece and the students that I've tutored over the years, there's no effort spared in trying to make math "fun". If anything there's perhaps too much distraction caused by attempting to make a connection with the students and a failure to clearly and logically explain the math.

I don't have the answers, but believe that it's incredibly helpful to track students, intervene when they show a lack of understanding and not let them slip through the cracks. I do agree with the OP that everyone is capable of math but it's a long journey and it takes a lot of practice.