Perspective (driven by shooting distance) is the goal to achieve, because wrong perspective can result in facial distortion as illustrated by this comparison (using 135 format)
In 2d photography all perspectives distort facial features that is the nature of capturing a 3d object in 2d.
It is possible however to choose a perspective such that the distortion introduced would appear most similar to the perspective of the viewer when viewing the image from a particular distance.
If your image viewing distance is greater a greater distance from the subject is required for this effect but if the image viewing distance is closer a closer subject distance would be required for this effect.
Nowadays people are very familiar with viewing images that are both shot from a closer and further perspective than is natural for the viewing distance as movie directors will do this intentionally for effect very frequently.
So there’s no audible gasp from the audience when a 180° fish eye lens is used inches from an actor’s face.
You can choose to distort the face as you see fit for your artistic vision and nobody will notice that you chose an unnatural perspective.
In fact many people prefer a perspective that is slightly closer than natural when viewing images of themselves as they feel it is more flattering because it makes them look thinner.
Most people don’t like to see the “the camera adds ten pounds” look of a more distant perspective on their own face. Especially since they’re used to seeing their own face from about 2 feet away in the bathroom mirror