How exactly does AM/FM carry both pitch and loudness of voice?
Voice has both pitch, i.e. frequency, and loudness, which are two separate analog data streams.


No. Voice is transmitted initially as one analog 'stream' of sound pressure waves in which the air pressure variation amplitude corresponds to the volume (at that instant) and the rate of change gives the pitch.


  No tutorial ... explain[s] how both aspects are transmitted over radio schemes that apparently can only take one degree of variation, ...


The AM and FM modulation schemes are analog and are called analog because the modulation is analagous (adjective, comparable in certain respects, typically in a way which makes clearer the nature of the things compared) to the original signal - voice or music.


  But I am also curious as to why this next obvious question that never seems to arise to the people making these tutorials and explanations, nor is the answer easily found out there, as I've been fruitlessly searching.


Maybe there's an opportunity for you there when you figure it out.

The tutorials demonstrate the results with sinusoidal signals because otherwise it would be impossible to see the modulation of a complex signal on a reasonable scale on a diagram.



Figure 1. The Simplified analysis of standard AM from Wikipedia goes a little bit of the way to describe what you are asking.

Notice in the illustration that the waveform is not sinusoidal but is an arbitrary waveform. Notice also that the amplitude modulation just follows the signal waveform. There's not much more to it. The microphone will convert the voice into an analog electrical signal and the modulator will modulate the carrier analogously too.