Nope the price is based on the 4C's... color, cut, carat and clarity. Cutting is a big deal, it takes a real artist to do it properly and done wrong a beautiful diamond can become worthless. Diamonds which don't make the grade become industrial grade diamonds, thus the supply of quality diamonds (meeting the 4C's) is low and the better they fall on the 4C's the more expensive the stone.......
Popularity is a result of the De Beers and a massive advertising campaign (and a bit of hording, too). So to return to the original question: why are diamonds so expensive? Lack of real quality and demand resulting from an effective marketing campaign.