Perception of women's vs men's bossiness compared to high-pitched vs low-pitched people's bossiness

A current thread about the word bossy, and the quote that
“A man with a forceful personality is more likely to be described as driven, confident, assertive, and a leader. A woman is more likely to be described as bossy, pushy, or a bitch”
reminded me of a possible theory why this might be the case (if we assume for the purposes of this discussion that it is indeed the case).

Is it possible that it’s not men vs women but people-with-low-pitched-voices vs people-with-high-pitched-voices?

That is, in general, adults have lower-pitched voices than kids, and it’s more normal to be taking orders/directions from an adult than from a kid. So, is it possible that when a high-pitched person gives us orders/directions, subconsciously it sounds like we’re taking orders from a kid, and we react badly to it?

If the above were true, we would consider men who have high-pitched voices to be more bossy than men who have low-pitched voices (given the same type of behavior), and I think, anecdotally, that might be true. Also, we would consider women who have low-pitched voices to be less bossy than women who have high-pitched voices (given the same type of behavior). Is this the case?

Any experiences/anecdotes/studies on this?