a complete radical independent thinker, and for some reason math, especially algebra was FUN for me. After being shown the basic rules of the language I took off with it on my own.
We are all different. Not a good idea to form too many rigid categories for others. I am in no way the non-thinking person you describe. Quite on the contrary.
Math including algebra is just another language and it has rules for usage just like any language has. I think it should be an option. If you want it, need it for your career, or like it, then take it. I needed algebra for my degree. Algebra was and is the language of science and research.