James Clerk Maxwell originally used quaternions in his work on Electromagnetism but there was a dispute/difference of opinion regarding their use that led him to use vectors later on. As Dr. David Hestenes points out in his many writings on Geometric Algebra and Geometric Calculus, quaternions...
quantum over classical
I think you do have a point. You might find the writings of Professor Edwin T. Jaynes to be of interest. I don't recall the exact papers but in several of his papers discussing quantum mechanics, which he was quite competent in as a research physicist, he noted that often...