which are also notoriously mined under horrid conditions - i.e. “blood diamonds”
Not only are blood diamonds mined under bad conditions, they are mined in mines owned/controlled by insurgents and terrorist groups, and then the sale of these diamonds is used to fund the activities of these groups. Watchdog organizations are a lot more careful about blood diamonds these days than they were 20 years ago, but it's still possible to accidentally get ahold of one. That's why it's so bad to buy one and it's why people all over the world made a fuss about them back around 2000 - 2003, because buying one directly funds atrocities in central Africa. They're usually sold cheaper than the monopolized diamonds too.
Don't forget that there used to be literal assassins that would kill you if you tried to sell (as a retailer, obviously the resale by individuals was so small-time they didn't care and hard to track) under the price you were told to sell it.
The short answer is, diamonds are controlled by a cartel with literal warehouses of diamonds kept off the market to maintain artificial scarcity, compounded by very successful marketing to increase the perceived value above actual value, raising demand. If you are buying new diamonds, you are always paying too much, although how much extra varies.