Cutting the ring on a designated place would allow to remove the ring from a finger in case of an emergency. But you can’t cut the ring in a random place, because of the battery.

Imagine your ring needs to be cut off while you are in the hospital: without knowing where the battery is placed it is a guessing game for the doctors where to cut the ring. This is a risk, because when the battery gets cut it will react with the ambient oxygen in the air, causing a fire which is hard to put out, since it can’t be extinguished easily.