Excellent points. And any trained actor could confirm this - voice pitch, phrasing, rising or falling tones, enunciation, pace, pronunciation - all of these things added together can very precisely define who we are - and yet, we can (with just a bit of practice - significantly alter that perceived definition. If these can be altered - then is there such a thing as an "original" or "natural" voice? I think that's only true to the extent that one is limited by things like dentition, resonance and the structure of the vocal chords and windpipe. Psychology of course plays a role. Presentation naturally biases toward your preferred brand of salsa. In other words - you might hate your "gay voice," but ... it's also your IRL shortcut and social filter.
I have to say I don't think there is a natural voice, in that while your physical make up may limit your possibilities, your voice has been influenced by your childhood, the languages you speak, the particular variants of those languages you use, and your age and background. How could you disentangle all of those factors to find a natural voice? And which factors if any are the 'natural' ones?
The ones that you can't easily change, I'd say... the ones that you can't change without being someone else entirely, with or without the aid of surgery. But to argue against myself, I think the most useful definition is "the voice that seems most expressive of who you naturally feel you are." A profoundly banal insight, that is.