This position paper delves into the transformative role of Geometric Algebra (GA) in advancing specific areas of Computer Graphics (CG) and Extended Reality (XR), particularly in character animation, rendering, rigging, neural rendering, and generative AI-driven scene editing. Common CG algorithms require handling rotations, translations, and dilations (uniform scalings) in operations such as object rendering, rigged model animation, soft-body deformation, and XR simulations. Traditional representation forms such as matrices, quaternions, and vectors often introduce limitations in precision and performance. Recent breakthroughs in the use of GA suggest it can significantly enhance these processes by encapsulating geometric forms and transformations into uniform algebraic expressions. Furthermore, we explore how GA can serve as a unifying mathematical substrate for neurosymbolic XR scene authoring, bridging learned neural representations and explicit geometric reasoning.