Well, specifically for an engagement ring, "I'm cheap" is the opposite of the message you want to send. There's lots going on at the interpersonal level that's all about "You're worth it" (and "I can afford it") that isn't about cold, rational utility calculations at all.
I think it depends on the person's mindset. My wife was thrilled that I got her a CZ instead of a mined diamond, specifically because she is against the atrocities of the diamond trade. I feel the same so it was a no-brainer. She would have had less respect for me if I'd given in to DeBeers' propaganda and marketing, not to mention the financial folly of spending a chunk of my savings towards a sentimental rock.
I think that there's a lot of bigotry to eradicate in the business of engagement. If, in order to get married, you need to give an impression of wealth you are essentially condoning a modern wife-buying practice. With the caveat that you're not even obtaining a dowry in exchange.
