Diamonds are just a special form of carbon which is, itself, not very rare. Granted, it's fairly hard to coax carbon into that form, at least if you want something that looks like a gem, but we already have CVD processes which can make diamond.
The main reason they're valuable is due to marketing.
Good link. It's a super old story [1982] but the information in it still stands the test of time. It's a great read into how the PR departments of DeBeers influenced entire countries (e.g. Japan) where diamonds previously held little/no value.
Yup. Producing several megatons of diamond in labs would be many orders of magnitude easier than harvesting it from another planet.
Even if it were the moon that were made of diamond, I strongly suspect that the energy requirements to harvest it would still exceed the normally-extreme energy requirements of growing it in a lab.
You raise an interesting idea here. I wonder how difficult it would be to harvest diamond from a diamond planet. Diamond can be cleaved if you hit it at the correct angle [1] but if the entire planet is made of diamond then what would happen? Would a wrong cleave or heavy force shatter the planet into nothingness?
Rather, I think the planet is made of many small (relative to an entire planet) sized diamonds embedded in dirt.
Given that making diamonds in a lab is cheaper than mining it right here on earth, it's hard to see how it could be cheaper to fly hundreds of thousands of miles through outer space to mine it.
The main reason they're valuable is due to marketing.