99% of modern physics was developed for pen & paper mathematics, not numeric simulations. Even when computers became readily available it was seen as somehow "less than" symbolic solutions. More practically, special-case solutions that were tractable symbolically require far too much computer power if approached from a fully general "local" simulation perspective.
QED is essentially a Monte Carlo simulation, just like ray tracing in computer graphics. The difference is that QED will correctly model diffraction (and other more complex physical effects) that the simplified graphics-only model doesn't bother with.
Both QED and raytraced computer graphics rely on a mathematical dualism where a wavefront can be tracked either as a surface OR as a vector perpendicular to the wavefront. The whole "summing up but mostly cancelling" is just accounting for the wavefronts. The use of complex numbers is mostly also just a method for tracking the cyclic nature of wavefronts.
If you skip the "waves" part, it becomes traditional computer graphics. Less accurate, but essentially the same.
Computer graphics could also simulate light transport by using a 3D volume, which is roughly speaking how some diffuse light simulations work in real-time games like the Unreal engine. The problem is that to get decent accuracy, you need a lot of memory to store that 3D volume. For low-resolution scene lighting this is fine.
Monte Carlo enables a solution to be built up incrementally with much less memory required, needing only a 2D accumulator in the image plane instead of a 3D simulation in object space. This allows a vastly more complex and detailed simulation to be calculated, which is important for the tiny wavelength of physical light instead of some non-diffracting idealisation of it.
For a physics problem the memory requirements of any non-trivial system would be gigantic, that's why everyone just ignores this approach even though it makes a lot more intuitive sense.