Some MTF transpeople opt for vocal chord surgery (not many, AFAICT, due to the cost and the fact that other techniques work well enough for most people).
From one company that offers it:
Most transgender voice surgery performed is feminizing voice surgery. In order to affect pitch, voice surgery is used to modify the physical characteristics of the vocal cords that determine pitch. These are vocal fold tension, length, and mass
FTM transpeople develop deeper voices just due to taking testosterone, which affects the aforementioned “vocal fold tension, length, and mass.”
So basically men have deeper voices because they have a lot more testosterone than women, so deep voices are likely an accidental of evolution rather than something specifically evolved.
However, it might have been accelerated by sexual selection once it became obvious that deep voices not only indicate masculinity, but adulthood, and in men it seems that appearing definitely not childlike is strongly selected for.