Multiple propeller shafts as a survivability choice

Is a single propeller shaft simply a cost-cutting measure?

The period matters. Most early steamships had a single shaft, while modern navies generally favor multiple shafts for survivability.

A single shaft's significance depends on the period. Most ships in the early days of steam used one shaft, so that arrangement alone does not establish that a design was a cost-cutting exercise. Modern navies tend to favor multiple shafts because they improve survivability.