Something that I've been wondering about is whether the original development of quantum mechanics involved a simple "mixup" due to the duality of the mathematic

Something that I've been wondering about is whether the original development of quantum mechanics involved a simple "mixup" due to the duality of the mathematics involved in wave mechanics. Imagine implementing a QED simulator: some EM source emitting billions of photons, each with a vector clock rotating to indicate the wavelength. You could code this up as an array tracking each photon. Alternatively, at very large numbers of photons, you'd notice that each pixel on your screen would have so many (maybe millions!) that you could just simulate the aggregate behaviour of each little square patch of space instead of individual particles. Ta-da... it's a continuum. No particles. You can simulate waves in space either using a Monte Carlo particle simulation or by subdividing the space into finite elements and tracking exchanges over their boundaries. Superficially the maths looks different, but the result is the same, and the finite element method has locality and makes the speed of light limit manifest. Why do we keep insisting on covering only the particle model in text books?