First, expensive rings are one of the main reasons why ordinary people don't wear them.
In ancient times, as one of the symbols of nobility, rings were mainly worn by many nobles, so their prices were much more expensive than ordinary stones or other gold and silver jewelry. In the eyes of many nobles, such gems are beautiful and worth collecting, which also raises the price of rings on the other hand. This has led to many ordinary people actually want to buy rings, but they are discouraged from such high-end luxury goods and would rather give up such things than buy them. So in most cases, they will give up buying rings and choose something more practical.
Second, the suppliers of rings are mainly nobles, and the literati have little contact with the general public.
In China, the traditional ancient ring did not exist at first, but became a popular item with the influx of many foreign businessmen and foreigners. For most people, the person wearing the ring must be a dignitary or a local celebrity. Compared with ordinary people, such things are high officials or status symbols, which do not match them. They don't think this kind of thing is worthy of themselves, so they won't choose to wear a ring, a high-end product. This is why there were few ordinary people wearing rings in ancient times.
To sum up, ordinary people in ancient times seldom wore rings, not because they didn't want to wear them, but because they didn't have enough money to buy them. On the other hand, more importantly, it is a symbol of aristocratic rank. As ordinary civilians, they are not qualified to wear such things.