Effect of impurities on melting point
In the old fashioned process, we used buttermilk sugar and a bit of vanilla. We put them into a churn (which is just a small bucket with a mixing blade in it so you could hand mix the contents) and then added ice around the churn (outside the churn) to cool it down. And then you mixed and mixed and mixed and mixed. But there was a problem. As the ice melted, the water it created was at $\pu{32°F}$ and even though the ice was colder (a commercial freezer is often about $\pu{15°F}$ (but a home freezer is warmer)) the water kept the churn at around (usually above) $\pu{32°F}$ ($\pu{0°C}$). And ice cream (being an "impure" water mixture) is a liquid, not solid, at $\pu{32°F}$. So, this wouldn't work. Enter salt. If you added salt to the ice, then the ice would melt well below $\pu{32°F}$ and be able to cool the churn to the freezing point of the ice cream mixture (I think its about $\pu{25 °F}$, but my memory shouldn't be trusted). So, the salt and ice form a salt water mixture which can be well below $\pu{32°F}$, and so can cool to below $\pu{32°F}$. If you were to add salt to the recipe, then you'd have to cool it even MORE to get it to freeze (although a little salt makes it taste better, imho). So, salt is added to the cooling mixture and (supposedly) not to the recipe's ingredients. I guess I should point out that you need to consider walking over hot rocks vs walking in say an inch of water at the same temperature. Which would burn you faster? There's no question that your feet would have more contact with the water than the solid rocks, so your feet would be more damaged by the water (water at $180$ or $\pu{200 °F}$ WILL burn you). My point is you actually WANT the ice to melt into a salt solution, because that will better cool the churn - as long as there's enough salt so that the liquid is cold enough.