Mathematical concepts are usually pretty intuitive. I think that the problem is more the notation that we teach than math itself being unintuitive and difficult.

I'd also say that programming is a mathematical endeavor by nature; logical manipulation is a branch of mathematics. If you're working at a level of abstraction where you aren't specifying logical manipulations, then you're filling out a template, not what I'd call "programming".

If all you're writing are CRUD apps then maybe you won't need it, but try doing graphics programming without mathematics. Which will be most interesting for children?

I learned basic trigonometry early (with a textbook and some advice from a school mathematics teacher) for the purpose of rotating vector graphics in BASIC to make a Spacewar clone. I expect there are many people who learned about complex numbers because they wanted to draw fractals. And linear algebra can sound boring until you realize how useful transformation matrices are in graphics programming. Programming is a great motivation for learning mathematics because it's so much more fun when you have mathematics skills.

"High level abstraction" is mathethematcs.