[tylerhou]

Here is another way that I thought of it.

1. To make ice cream, we need to cool milk/cream below the freezing point of water (because milk/cream contains water).

2. To cool things, liquids have good thermal conductivity properties, so we would prefer to use a liquid.

3. We need some substance which is still a liquid at slightly below freezing.

4. It happens that salted water has this property and is relatively cheap.

[majikandy]

Remember for point 4 it needs something in that salted water that can keep it at the lower temperature.

[tylerhou]

Also, we would like a phase transition slightly below freezing so that it's easier to keep a stable temperature.