This limits the supply, but we also must remember that the reason there's enough demand to justify the diamond industry to do this kind of shady stuff is due to marketing. I seriously doubt that diamonds, and especially natural diamonds, would be as popular as they are without the marketing, since the lab-grown ones are indistinguishable in all but price, if one wants one.
Famously of course, marketing is responsible for the relative prevalence of diamond wedding and engagement rings. That they'd have to be worth N months' or years' salary? All marketing. And it has clearly worked, given how prevalent it is. And it has worked so well in fact, that this very idea has been embedded into wide parts of Western society.