The problem is that educators know very little math. They don't know how it's used in real life.
One of my specialties is curved surfaces for geometric modeling. I write software for shape design and analysis. I once had to write a routine that would find the intersection of two tensor product polynomial surfaces. This has to be done algorithmically, and there are lots of methods given in the literature. It would be stupid to ignore those solutions just to discover my own. I'm not proud. I'm more than willing to copy what someone else has done, so I studied the literature. In fact, if you write a technical journal article, you better show that you have a full grasp of and reference to all other key articles and books. If you ignore the literature and (re)discover a technique, then it either won't get published or it will get trashed by your colleagues. Ignorance is not treated lightly. Prior art reigns supreme. (knowledge and skills)
However, nobody had a solution that met my need for speed of calculation. I had to create my own solution, but I don't start from scratch, and I don't use some sort of pattern recognition or critical thinking to find a solution. I use my toolbox of mastered skills. First, I have a fast way to convert each polynomial surface into a large set of triangles. All I needed next was to find a very fast way to determine if any two triangles intersect. I don't "discover" a solution. I look at the problem and see how my toolbox of mastered (rote) skills can be applied; vectors, dot products, cross products, parametric equations, different forms for defining plane equations, and matrices.
These skills don't exist in some sort of rote or out-of-context space. They have a meaning and a use. Two independent vectors define a plane. If I take the cross product of the two vectors, I have a new vector that is perpendicular to that plane. I didn't discover that. I was taught that.
Don't educators understand that being creative mathematically requires a whole lot of basic, mastered skills? The larger your tookbox of mastered math skills, the more creative you will be.
I don't know why they have this rote or script hangup. They just don't have enough understanding of math to know if anything they do is correct or incorrect.