The whole point of Algebraic Geometry is to describe geometry using algebra. It’s is a very deep, successful and important subject in modern mathematics. I wouldn’t say it needs to recover it’s geometric routes, it’s sort of the whole point. To describe something geometric you actually just need to describe algebras of functions on that object. It’s a very rich subject.
What happens at school and early uni however is a different story. Classical algebraic geometry could definitely be taught to undergrads or high schoolers but there is some weird insistence on only calculus being important. If anything the categorical and algebraic ideas expressed in lots of algebraic geometry follow through into all sorts of other areas of mathematics. I think there are even connections to modern physics. Id say it’s probably one of the more important areas, but it’s relegated to later stages.
What happens at school and early uni however is a different story. Classical algebraic geometry could definitely be taught to undergrads or high schoolers but there is some weird insistence on only calculus being important. If anything the categorical and algebraic ideas expressed in lots of algebraic geometry follow through into all sorts of other areas of mathematics. I think there are even connections to modern physics. Id say it’s probably one of the more important areas, but it’s relegated to later stages.