symmetry happens in a variety of dimensions simultaneously. look at fractals and tell me symmetry doesn't have its own form of beauty. complexity and pattern are beautiful of their own accord. the reduction of symmetry to only a few dimensions is what creates a mechanistic, unnatural, alienating notion of symmetry. because life is the production of difference within a cyclical symmetry machine built by that difference.
as for the face, features can be beautiful in so many different domains of ideals. babyness (who doesn't love babies?!?!), trend, affluence, iconography, sexual dimorphism, skin health, facial symmetry, jaw, big eyes, a button nose, voluptuous lips, pursed lips that show focus and power, squinty eyes and the whole-body whole-face affectation that is so emotionally contagious that you can't say no to it or shut it out, self-assuredness, complexion, ethnic variation, hair color and texture and movement, etc.
i also think face typing personality wise can be done with reasonable accuracy. i would never use it as the sole piece of information, but i think each type has their own kind of beauty profile. and i think there are a variety of ways of creating such schemes that all happen simultaneously and blend into weird living breathing patterns of symmetry and sway.
