To completely ignore the tone of your post, and reply to the topic at hand, it isn't "clearly sensible". Even if your only motives are driven by profits, it takes a lot of money to retrain a replacement. Add to that the motivational benefits of providing an employee with support during a time of need, which will statistically provide greater productivity in the future, and it's usually better in the long term for a company to support employees in need.

I'm frankly disgusted that anyone would look at this from a purely profit driven viewpoint, especially as this viewpoint is short-sighted and mistaken.

Treat your employees well and they will usually treat you well.