Algebraic geometry / differential geometry are both treated as “sophisticated”, “advanced” subjects. They typically require high-level preparation (several years of pure math courses as prerequisites) and are taught in an extremely abstract way, often are deferred to grad school, and are seldom if ever taught to non-math-major undergraduates.
But geometric algebra, a.k.a. real Clifford algebra (“geometric algebra” was Clifford’s own name for it), can easily be taught to high school students in a very simple concrete way, and then used throughout science/engineering/computing courses aimed at non-math-majors. It can unify and simplify the wide variety of other mathematical formalisms that are used throughout undergraduate technical curricula. It is straight-forward to implement in a computer, and it makes calculations much easier to write down.
The way GA is promoted by the non-math world does not unify mathematical formalisms. I've yet to see a GA implementation that does more than reimplement rotations/quaternions.
But what is implemented in computers is not 1:1 with the algebraic tools that can be profitably employed to solve geometry problems symbolically. GA is a rich language full of useful tools which can describe/model many kinds of problems.
But geometric algebra, a.k.a. real Clifford algebra (“geometric algebra” was Clifford’s own name for it), can easily be taught to high school students in a very simple concrete way, and then used throughout science/engineering/computing courses aimed at non-math-majors. It can unify and simplify the wide variety of other mathematical formalisms that are used throughout undergraduate technical curricula. It is straight-forward to implement in a computer, and it makes calculations much easier to write down.