I want to emphasize that the question of the subjectivity of beautyis distinct from the question of whether there are rules or principlesabout beauty. Many aestheticians are particularists. They believe thatthere are no general rules or principles governing what makes thingsbeautiful, and that what may count towards beauty or aesthetic merit inone context may be aesthetically irrelevant in another context (or mayeven count against overall beauty or merit). But this is consistentwith such a view that judgments of beauty are more than merelysubjective.
Kant is famous for having arguing that there can be no rules or principles of taste in his Critique of Judgment.Interesting contemporary discussion of the possibility ofgeneralizations regarding beauty and artistic merit can be found inMary Mothersill's book Beauty Restored. Mothersill isskeptical of there being any interesting generalizations here, but I'mnot convinced by her arguments.
What about the principles of design that are mentioned in the question? Particularists will think these are just rules of thumb--useful but ultimately inaccurate generalizations. I'd be interested in finding out whether there was evidence that they are accepted cross-culturally. If they were, there might be some reason to think that there was some broadly evolutionary explanation for them. In the end, the question of why certain generalizations about beauty and our visual preferences are true--if they are true--seems to me to be an empirical question. That is, the answer to it would await serious scientific investigation.