The models EE use are simplified, drift and diffusion current and electron and holes with their different mobilities and energy levels. Math apparatus used here, and strictly related to statistics, is limited to averaging, I would dare to say.
I think you can agree now that your original observation of statistics as "glorified curve fitting" as a bit naive.
On the basic materials level, density functional theory is the current gold standard, and it's extremely statistics heavy.
At the systems and architecture levels, you may be right, though.