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.