The cons are that you're funding a horribly immoral and corrupt industry that causes countless misery and death in Africa.
Not a huge fan of the diamond industry
Zeo, my father has been in the jewelry industry for over 35 years, and currently owns a store that deals in fine jewerly (precious gems, yes including diamonds..) and metals, and my sister is a certified gemologist with the G.I.A who has worked at the renowned JB International, whose sole purpose is to deal in high-end diamond jewerly sales. Both of them take their business very seriously (as do many others in the business...) in regards to where their gems come from. Going through reputable dealers, getting the proper certifications, etc helps reduce the chances of being associated with conflict diamonds greatly... Of course no QC process is perfect and some will get through.. But you shouldn't generalize an industry based on a specific scenario...
That's as if people who dislike Bitcoins categorize everyone who uses as criminals because it is used for sites like Silk Road, and provide possibilities for money laundering.
As for the idea of a BTC / Diamond|Precious gems, I don't see why a service such as this won't come up in the future. Companies are already venturing into the BTC / Metals market, so it should just only be a matter of when, not if.