I think it is a combination of factors. Mathematical pedagogy is legitimate if the end goal is to train mathematicians, so yes it is geared towards those who think in the abstract. (I'm going to ignore the comment about very smart, since I don't think mathematical ability should be used as a proxy for intelligence.)
On the other side, I don't think those who are involved in curriculum development are very skilled in the applications of mathematics. I am often reminded of an old FoxTrot comic where Jason calculated the area of a farmer's field using calculus.
Frankly I wish I had known integral calculus going into geometry, I could tell there was a pattern behind formulas for areas and volumes but I couldn't for the life of me figure it out. There are worse ways to remember the formula for the volume of a sphere than banging out a quick integral!
I had known it. Thanks Dr Steven Giavat. The geometric shapes gave the patterns meaning. I read 'mathematics and the imagination' and mathematics a human endever' while I was starting algebra. Also the time-life book on math. All very brilliant because they used the methods that were used to investigate it, to show how it was discovered. These allowed me to fly ahead in math until I got to trig. Which took a long year to get facile, until I was able to finish my degree.
I had brilliant teachers.
Napier's bones, were for adding exponents, hense multiplication. Brilliant and nessary for the development of the slide rule, and the foundation of modern engineering, until the pocket calculator.
On the other side, I don't think those who are involved in curriculum development are very skilled in the applications of mathematics. I am often reminded of an old FoxTrot comic where Jason calculated the area of a farmer's field using calculus.