I think there are two main reasons why we don't see more of the applications of Geometric Algebra.
One is that most people who would be using it are already satisfied with Differential Geometry and the coordinate-free formulations of physical laws we have there already. Having done some work in computational GR, I haven't seen anyone mention it and none of the texts I have read do. I think for people advanced enough in their field they are already past any pain points that this solves, so they don't learn it and don't teach it to their students.
Two I think that the people who this is most useful for, students just starting out in physics, aren't really in a position to go out and learn a new representation for doing their problems in. Especially when they are struggling enough with the basic concepts and their instructor is highly unlikely to be familiar with it.
Because of those two things and the cycles they mutually perpetuate, without a huge PR campaign or some well known teacher using it at a big name school for an introductory class I don't think we will ever see this become popular
One is that most people who would be using it are already satisfied with Differential Geometry and the coordinate-free formulations of physical laws we have there already. Having done some work in computational GR, I haven't seen anyone mention it and none of the texts I have read do. I think for people advanced enough in their field they are already past any pain points that this solves, so they don't learn it and don't teach it to their students.
Two I think that the people who this is most useful for, students just starting out in physics, aren't really in a position to go out and learn a new representation for doing their problems in. Especially when they are struggling enough with the basic concepts and their instructor is highly unlikely to be familiar with it.
Because of those two things and the cycles they mutually perpetuate, without a huge PR campaign or some well known teacher using it at a big name school for an introductory class I don't think we will ever see this become popular