There was a cottage industry of exotic hypercomplex numbers that disappeared when linear algebra matured to eclipse them.
In fact, Maxwell's Equations were originally derived with quaternions.
And speaking of Maxwell's Equation"s" :
With some familiarity with linear algebra, it's easy to derive the formula for constructing a rotation matrix. You just have to think about what the operation does to the axes. The derivation for quaternion rotation is far more abstract, by virtue of the operation we actually care about involving a sandwich of multiplications with unclear 4 dimensional meaning.
Augmenting your space to handle not just rotations & scaling, but translations is easy for matrices, just requires a homogeneous coordinate and you get 4x4 matrices with intuitive columns.
Augmenting quaternions to handle translations requires the 8 dimensional dual-quaternions.
Another angle here, I remember seeing a study where some children were just... taught algebra. Like given high school algebra classes in 3rd grade, and kids were able to absorb all that abstract reasoning "just fine" (according to the study).
Of course there's only so much abstraction that can be done, but I think we shouldn't assume we are at the end of history on much of anything (except for parsing algorithms)