Diamond jewelry is a luxury good whose primary purpose is to signal wealth. A "discount diamond" inevitably fails at that purpose.
If you can't tell the difference, how does it impact signaling value? If you are optimizing for signaling value, synthetics are better since you can afford a larger and clearer one.
Pay less for a synthetic and admit it, and you've signaled a lack of sufficient wealth to buy a real diamond.
Pretend a synthetic diamond is real and you're deceiving people.
Either way the synthetic diamond is signalling something undesirable (to the target market for diamonds) precisely because it costs less.