In my first few semesters of studying Physics I found these commonly used integral identities (Stokes etc.) really odd and wondered why those look so similar. Of course EA/differential forms provide ways to generalize that. Then other QM topics have these absolutely counter-intuitive geometries, although GA seems to provide some consistent intuition. (E.g. why a full rotation is 720 degrees)

That said, I think vector algebra/calculus seems to be too much calculation focused to me. It's really hard to develop an intuition without excessive amounts of exercising calculations. (And books about GA still seem scarce)

By the way, this article provides some estimations about no. operations compared to just using matrices: https://enkimute.github.io/LookMaNoMatrices/