> There is no short answer as to what is fully going on here, but simply put, Python modules are packaged either as a Wheel or an Egg
This is a false dichotomy -- there are actually many different ways to package a Python module, including source distributions (sdists). These are just the two most well-known types of built distributions.
> The numpy module is a wheel, i.e. it is a source distribution that depends on a handful of system libraries — gfortran, blas, lapack, atlas — to compile properly.
This is not correct, a wheel is specifically not a source distribution, it is a built distribution. The dependency on platform-level libraries has nothing to do with what type of distribution it is.
NumPy publishes a lot of wheels for a given release (https://pypi.org/project/numpy/#files) each of which is platform-specific, since they are pre-built (pre-compiled) for a given platform.
In the event that a built distribution isn't available for your platform, that's when pip falls back on the source distribution, which requires the build step (hence the dependency on gcc or clang).