Don't scopes have that same "sweeping effect"? really old analyzers had slow sweep/sample rates ..the old long persistance green phosphor type?
Tone testing isn't going to tell you much, you really need a complex waveform like the human voice generates....or yes, some Van Halen
I find a spectrum analyzer a pain to watch while talking because of the sweeping effect. A scope is a lot easier to watch. A FFT analyzer is a lot easier. Spectrum analyzer is easier with tone testing.
John is right life is short and scopes are cheap.