Wolf, I don’t disagree, but I guess that can be a little confusing, so their way is a bit simpler (at the chupah; it’s harder to get such a ring). I was once an eid kiddushin, and the mesader (a well known posek) simply asked us if the ring was worth at least a p’rutah. I have no doubt that the other way (no karatage marking) is simply a chumrah.
Oomis, I asked because the OP was referring to engagement. Your mind is probably more on kiddushin now. 🙂 Mazel Tov.
Hebrew ring inscriptions/ engraving for wedding/ engagement ring
They probably wanted it to be solid so it’s easier for the kallah to get an accurate idea of the value (see my previous post).