AvE? Just hands.
Marco Reps? Just hands... wearing gloves.
LockPickingLawyer? Just hands.
BosnianBill? Just hands.
The Signal Path? Largely just hands, although he has appeared occasionally.
Wendover Productions? Disembodied voice.
CGP Grey? Disembodied voice.
Real Engineering? Disembodied voice.
Not to mention innumerable video game streamers.
Of course, disembodied voices aren't in-and-of-themselves a new cultural phenomenon: Radio has existed for years, as have podcasts. And there are TV formats like nature and history documentaries where the narrator may rarely or never appear on screen.
And even on Youtube, there are a number of female voice-only celebrities - for example "vtubers", where a female voice actor plays games while pretending to be a cute anime girl. Of course, one could say that's an example for the theory people want to see beautiful women, not against
As far as privacy it doesn't necessarily apply because the famous ones almost all have previous careers as face streamers, and their fans know who they are since they use their real voices. But if you are doing it to hide yourself then it works, and it means that everyone else can interact with you and seem to be in the same world.
https://www.youtube.com/user/featony
Although there was one where you did get to see his face.