The only worthwhile content of dot products is geometry?

of course. dot products are a symmetric form on vector spaces. they let you compute the spheres of radius r.

given the sphere of radius r, for any pair of vectors v,w in the sphere

    -r^2 <= dot(v,w)=dot(w,v) <= r^2

this is how we define parallel perpendicular and antiparallel.

the dot product is only meaningful in a geometric context. by definition it projects vectors down to scalars. fixing the scalar value finds the spheres, and for a sphere we can vary the vectors to compute cosines.