"Is it possible to be somewhat specific on the importance of each of these elements...."
I have always held good design (in any field, but specifically golf course design) to......hold in balance each of the three.
You use FUNCTION, SIMPLICITY, BEAUTY. I have always used a slightly different, yet parallel thought....
.....Is the design maintainable, can the best of the game be played, and is it aesthetically pleasing?
Like a three legged stool........all legs must fully function or else one is liable to fall! In my opinion that is never SITE or CLIENT dependent...it stands alone, as a truth of good golf course design.
Tom