Problem is that experts don't even necessarily learn the same way. People who become mathematicians are hurt, not helped, by the kind of rote learning that is necessary if you want to bring along people who hate math. There are a bunch of complex issues here but we need to start by acknowledging that what will benefit the students who will be most likely to use the material may not be the same thing that maximizes the number of students who can do the basic exercises. It's not pretty but sometimes there is a trade off between creating 10% of students who leave loving the subject and maximizing the number who can slog through it even hating it. Phonics is a particularly bad example here because the students who are quicker to learn to read or better supported at home don't learn to read in school so even if they learn (as many of us did) via whole word phonics is what should be taught in school. When you apply that same reasoning to teaching calculus you end up with no students who learn to love the subject and be creative with it and a bunch of students who learn to do rote computation they will never need to use.
