generally engineers in the real world have more than high school education.
high school is best used teaching kids *why* the maths works. this gives them the understanding of what they are using.
highER education can then focus on the *how* best to implement this knowledge (as well as obviously building on it) in the 'real world'.
do you focus your time on a preteen-teenage kid teaching them soon-to-be-redundant-technology specific skills, or do you focus on the arguably harder to teach but more beneficial in the long run understanding of what the technology is doing? when i went through high school graphing calculators were forbidden in exams for this exact reason (and discouraged in class as well).
the idea of maths classes at this level is to learn the maths, not churn out solutions at machine like rates (although some maths 'teachers' seem to forget this).
by your 'charcoal shovel' logic, why teach math at all? most people use computers or cash registers to tell them the answers to those number things. they may not use charcoal and shovels, but they *certainly* use the same concepts at that stage. are you suggesting giving graphing calculators to preschool kids? yes, i know you were probably exaggerating, but the point remains.
knowing *WHY* a formula is used is more important than *WHAT* formula at this stage. engineers aren't the only people that need maths.