It still always feels a bit paradoxical to recognize that quaternion algebra was invented before vector calculus and to fully realize how new linear algebra really is. Hamilton was really way ahead of his time.It's interesting that Tong listed quaternions as part of Hamilton's unhappiness. In his days they were a great success for him as a respected mathematician. It was considered even a kind of rebellion when some people started to use vectors, among the first Heaviside, Gibbs, and Helmholtz ;-).
I have a feeling that I'm in a small minority of physicists who have a strong aesthetic preference for quaternion algebra over vector calculus for non-classical physics, seeing how neatly it dovetails with the spinor calculus and the theory of differential forms, while the limitations of vector calculus are by now painfully obvious.