Diamonds are worthless, but reject them at your own peril. When my friend proposed to his girlfriend of 3 years, because the ring didn’t have a diamond she said no.
Sounds like your friend dodged a bullet there.
(I proposed to my now-wife without a ring. After she said yes, we went shopping for one).
If that is true, then buying something more expensive than the usual thing doesn't invalidate any of the arguments against diamond engagement/wedding rings.
If emeralds are cheaper, then while I'd rather have the emerald anyway (it's prettier to my eyes), I can't see any person (male or female) preferring the cheaper jewelry.
"Should we spend $X of our now common budget on a ring, or spend $Y < $X on a ring and buy a nicer car/pay out the house faster/add some more to the kids college fund?"
If she says "the ring" to that, consider a replacement.
Less damaging to his ego?
A woman rejecting a man because the ring was not good enough portrays the woman poorly.
A woman rejecting a man because she can do better portrays the man poorly.