Perspective of a wife here:
You need to do something together that reflects your joint values. If she wants a fancy, expensive ring, but that doesn't comport with YOUR values, that's a problem.
My husband truly surprised me with his wedding proposal. But he knew me well enough that he proposed with a very pretty CZ ring he had bought online for, like, $25. Read up on the history of the stone--it used to fool jewelers until they learned what to look for. NO ONE, and I mean NO ONE, will be able to glance, or even stare hard from up close, at your wife's ring and know it is a CZ.
Then consider the history of diamonds--including the modern history of how they are mined, and the devastating and appalling human rights atrocities that surround their production.
In fact, after I gave an enthusiastic yes to my husband, after a few days I explained that as pretty as it was, I didn't really want the CZ ring either. I didn't want anything thinking I would wear a diamond, to be honest, given what I've written above. Again, the question is--what comports with your values? To me, "advertising" a diamond even though I wasn't wearing one wasn't acceptable. So we picked out a pretty, but under $100, etsy ring with a blue stone.
After we got married, I even stopped wearing that--because again, jewelry that looks expensive (even if it isn't) also just doesn't comport with our values. I now wear a simple titanium (I think) band, and my husband switched over to a black silicone band for comfort/safety--which cost about $2, and he gets no end of compliments on it. I had one for awhile, too, but it stretched and fell off. I'll probably replace it at some point, because I loved it!