Each item is unique. A ring is a single object with its own cost, weight and stones, and a system that counts products rather than pieces cannot tell what is actually in the safe.
Customer property is the sensitive part. A watch or a ring left for repair belongs to somebody else, and knowing exactly where each piece is, at every moment, is both a legal and a reputational necessity.
Repairs travel. Work sent to an external workshop leaves the shop's control, and a customer asking where their grandmother's ring is deserves a precise answer rather than an approximate one.
Valuations are consulted long afterwards. A document produced today may be needed after a burglary in six years, and the record of what was described and photographed is what makes it useful.