That tradition is news to me. As far as I knew, the tradition is to give a ring with a stone (commonly diamond) for engagement, and then a plain band for the wedding. Once married, only the plain band is worn.

The reason: stones can snag on clothing, rip an eyeball, snap off, attract violence, or scratch something you care about.

I went with my birthstone (Arizona Peridot, cheap and pretty) from my grandma for the engagement. My wife thought that was sweet. She keeps it in a drawer somewhere as a memento, and wears a plain gold band every day.

I suppose I might prefer titanium over gold, for weight reasons, but the gold is OK.