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.

It's really not, because all your other staff will immediately consider leaving, and some actually will. You'll then face the cost of hiring and training replacements, which is very likely much higher than giving the original staff member three days off., not to mention the potential fallout from the negative publicity it might entail (like this thread).

There is no benefit to running your business this way. It's only harmful.

Real talk, I've worked for some horrible employers back home in Wichita, but -never- has any fired me for taking time off due to an emergency. If anything, they said, "go and take care of it." And that was that. I don't know what part of the world you come from but even in Kansas (a very socially and economically conservative state) we don't haggle people over three days off for an emergency. We suck it up and deal with it.