Huh... IMHO I hate it whenever JAV studio put mosaic on, no matter it's genitalia, male/female face, bystanders, street signs, or logos on cloths and products (e.g. beverage)
But it's technically an interesting request. I was thinking there's probably open source face detection algorithm out there. And blur/mosaic is easy to apply (any Photoshop or movie editor would offer many filters).... But
@NoToRo suggestion is in right direction, I'm not familiar with Da Vinci Resolve... looks like another alternative for Adobe Premium. My own choice in this category is kdenlive (for Linux). These are all movie editors so they are not specifically design for your need. But some of the functions in those powerful program may do it.
Looks to me quite a major effort.