The beauty line doesnt work, because then platinum shouldnt have any serious value despite its rarity (it just looks like silver basically)
The industrial value is laughable, but read comments below/above to debate that more at length.
The scarcity line doesn't work, because you have elements like bismuth which are also (Arguably) more beautiful than gold https://66.media.tumblr.com/61ce390242a79a767772d4b2027eb902... but command prices far less despite being .025 vs .0031 on the PPM abundance on earth. Or even look at ruthenium which has a similar look to platinum and is even rarer than gold. Did I mention it also goes for about 400 an ounce? Quite a savings over gold.
The only thing that makes sense is that we as a collective have decided gold has value of X.