As an EE, how would you explain concepts like a PN junction or field effect transistor without using statistical mechanics? (Ie, expected behaviour for ensembles of huge numbers of particles).
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.