In the absence of an answer, I gave it a go.
All the bits of the signal path that are meant to be linear test out just fine with a VNA. From the mic cable through to speaker terminals (which obviously need quite a bit of attenuation when driven by an amp).
Once I go out an "air interface" into a room and mic the results are horrible. It takes a huge number of sweeps to start to see what is going on.
I'll give it a go..
they are both essentially doing the same thing: applying a stimulus to the input of a system and watching the response at the output, at multiple frequencies
the biggest difference is that your typical lab VNA will measure a single frequency at a time, and if you like it will do a sweep and log the results. These results are accurate, but noisy so they are useful for seeing trends or letting you know if your circuit is unstable.
Although most dual channel FFT software packages can be made to work exactly like a VNA nobody does because as you've found out it's a PITA
Smaart and others have options to use averaging (from small averages right on up to many seconds) and smoothing. as well as many other little tricks like time windows to avoid unwanted signals from getting into the measurement.
FWIW your results would be the same with Smaart.. cables, electronics etc all measure great with nice clean responses (as they should) and speakers/rooms measure comparatively terrible.
If you were in an anechoic chamber the differences would be more subtle.
Jason