There's also this thing with having a "soft voice", that's something much more often attributed to women than men (IME – can't remember hearing that said about a man, like, ever). But in a relatively quiet environment, I pretty much never notice any difference in loudness, nor on recordings, and it's definitely not a shyness thing. But they still get drowned out much, much easier in public spaces than my own male voice, and it's visibly frustrating having to almost scream to just be understood while I can talk normally. That was a pretty regular thing during lunch break for a while when I worked in a team with several women who had that issue.
And finally, while I may be really weird in that regard and everyone else here just processes content and not the voice that's talking, but female and male voices really do have very different emotional coloring for me. I think my native country is still a bit behind when it comes to ubiquitous disembodied female voices, but I'll readily believe it works, and I don't have difficulty imagining the emotional part of the message hinges at least partly on its femininity.
The "soft spoken" is used for men.
In a public environment, the majority of the lower spectrum of sound is flooded with the surrounding noise what means that if a low pitch noise is used it will barely be understable. High pitch voices are well better in theses cases because it uses the less busy part of the sound spectrum resulting in clearer sound. There is nothing to do with gender and patriarchy.