Consider this article:
http://www.theatlantic.com/doc/print/198202/diamond
I believe the problem the article describes, the lack of a secondary market in diamonds, still exists. However, the article was published in 1982, and the prediction of collapse in the diamond bubble didn't happen.
Consumers without the necessary knowledge and connections are probably taken for a ride. Dealers would exploit their lack of knowledge and options, just like 2nd hand car dealers offer terrible prices for cars - they know that if you're there at all, you're desperate. In this market, everything is sold at auction. Going to a dealer by yourself is holding a fire sale auction with 1 bidder. Of course you lose.
Between dealers, or high end customers with a dealer acting as their agent, selling for-real quantities, the market is much more stable, consistent, and liquid. Unless you want to be utterly ripped off, you must buy at a proper auction and sell at a proper auction too. You can say the same about pretty much any other store of value in the world, by the way.
But all this is obvious; if diamonds really did lose half their value every time they changed hands, no-one would bother - and yet they obviously do.
By the way, I agree wholeheartedly with that article - which I read years ago. I think I read it in the actual magazine! Anyway, yes, the value of diamonds is almost completely illusory - it's wholly artificial and if if the real supply were ever released to market, value would plummet. However, that hasn't happened, the consensual hallucination that compressed carbon is worth a lot of money stands, and you can buy and sell diamonds for a lot of money. I don't see this market changing anytime soon. It is in no-one's interest to break the spell.
And if you got rid of diamonds, people would just find something else with an agreed value. A lot of people need this kind of currency. Until crypt.kk comes online, of course.
You might as well ask who's dumb enough to steal gold.
And yes, I know that the value of diamonds is largely artificial. However, the current situation is, and is likely to remain for some time, that people think diamonds are valuable, and will trade them for actual money at a reasonably consistent exchange rate, anywhere in the world, no questions asked.
There's quite an interesting story in this whole system, actually. Diamonds have become a kind of underground currency in some circles. Unlike gold, they're not metallic, so can be transported safely by air. Unlike paintings (another other major money laundering commodity), they're small and not delicate. One could write an interesting analysis of the dynamics of such a self-supporting, consensual-illusion-becomes-reality of the diamond trade. It really is proof that if something is needed, people will make it.
Yes, it's carbon that has been compressed a bit. So what? The romans used salt as a currency! The point is, as of today, diamonds are an excellent currency to be paid in, especially if you have something to hide.