That actually works in meetings or other group situations when people seem ignore my points - deeper voice works better. Not sure why doing it would be shocking. It is tiring to do it all the time through. Men chage their voices based on social situations too.

It works also with students when you are teaching.

I am pretty sure she also carefully selected cloths and hair style to project the right image and thought in advance about what she is going to say. It is the same thing. That is what all charizmatic leaders, whether good or bad, do all the time.

Yes, agreed. However, this full-time is very extreme.

The same advice was given to, and taken by Margaret Thatcher

Also, from a few days ago:

http://www.bbc.com/capital/story/20180612-the-reasons-why-wo...

Not any less authentic than Elon Musk’s hairline. Nobody seems to have a problem with men spraying on hair from a can. Why shouldn’t a woman alter her voice?

is it actually possible to do this? I can't just deepen my voice on command, can some people do it naturally?

Not necessarily naturally, but it's reasonably easy to learn - it's ultimately the same underlying mechanism as singing different notes.