What secondary benefit did requiring replacement of an early blown fuse provide to utility providers?

It served as a powerful indicator that a significant problem occurred on the line.

Beyond its primary function of interrupting dangerous current flow, the fact that Murray's fuse was a one-time, sacrificial device provided an important secondary benefit, especially in the early, less monitored power systems. Requiring a physical replacement after a fault occurred served as an unmistakable and powerful indicator to utility personnel that a significant, non-transient problem—like a serious overload or a short circuit—had taken place on that specific line segment. This consequence was contrasted with a resettable device, like a circuit breaker, which might obscure the underlying issue by simply resetting and potentially allowing a dangerous condition to persist undetected.