I grew up southern baptist and I've never heard of this. It's kind of blowing my mind that people perceived as women would be told how to talk, but it rings true because I had similar things like no long hair or "walk like a man" and other things imposed on me.
In my experience as AFAB with a more monotone, less femme voice, I got 'you sound bossy' 'you sound like a bitch' or just ignored until I 'asked nicely' which meant 'sound subservient'.
It has caused me so much trouble in sounding authoritative, because I always had to be high pitched to be heard, but deep pitched to actually be listened to.
Framed as well meaning, oh-honey advice from older women, I've heard that or some shade of it at least 100 times since around 8yo, I don't think it's rare, unfortunately.
It went hand it hand with "the bellies that show are the first to swell", which my store manager said to me at 17yo, the comments that other girls should keep their boyfriends (my friends) away from me, all the weird punishing ingrained misogyny bullshit women do to each other in US gender culture.
As soon as I got secondary sex characteristics, I started getting in trouble for just, like, existing
If I could go back and do it again, I would fucking embrace it.
She should use that voice to defend her autonomy, and to sound like herself. Seriously.
I work in hard science IT, and as I shed my feminine vocal habits, my job is easier. People listen to me more. My life is better, I'm not forcing my thoughts through a Play-Doh mold of intonation.
It can absolutely be a skill, because it will set her apart!
I think part of the reason why a deeper voice is heard more might be because it sounds more sincere. The high pitched voice can sound a little patronizing and unnatural. It's the voice moms use on their kids when they want them to do something (like chores) but don't wanna yell at them. It's difficult to work with someone who you think is using a "nice" voice on you to try to manipulate you into agreeing and doing what they want, with the implication that you're angry and will be punished for not being obedient. That's what that tone sounds like to me.
Oh that's absolutely what I do now. I'm some shade of gender fluid/NB, and my phone voice goes so high pitched when I'm stressed that it makes me very uncomfortable. I'm rooting it out.
I'm amazed at how much differently people respond to me, depending on the gender mannerisms I use.