[spekcular]

I think your reasons are good and essentially what I would give. I also think differential forms are a much theoretically cleaner way to express the same concepts.

Further, teaching differential forms prepares my students to engage with the (vast majority of the) existing math and physics literature. Teaching geometric algebra doesn't.

The practical reasons boil down to: I have to teach the standard stuff because otherwise they can't read the literature. Having done that, what's the marginal benefit of teaching GA? Not a lot.

[ogogmad]

On the other hand, maybe GA can help with differential forms. Differential forms involves exterior algebra, and I feel like some aspects of exterior algebra are elaborated upon in an insightful way by GA. For instance, the grade-2 elements of an Exterior Algebra can be understood as angular velocities in many circumstances. In GA, this is captured by the exponential map that sends grade-2 elements to rotors. I don't know if this can be helpful for teaching purposes.