>We can’t change the area of contact between the ice and the metal tube containing the cream

We absolutely can, we can add salt. I have studied advanced physics, but more importantly I have been a professional chef and I understand how ice cream is made.

You can absolutely do this. You add salt.

That's literally why we add salt.

>Because the salty ice is colder

Ice does not get salty. Ice is a solid, and it is a unique solid which expands when it cools. Because of this property when you add any weight to it, it will compact, and melt.

If you don't agree with this, or can disprove this in some capacity then feel free to do so.

A cube of iron that is chilled to absolute zero, if stepped on, isn't going to compact any further. A cube of ice will.

>So yes, the freezing point is relevant.

How? Salt's affect on ice diminishes as the temperature drops. By the point we're talking about absolute zero the affect of salt on ice would be almost zero.

edit: I suppose the iron would compact slightly, but not to the magnitude of ice, and the energy transfer relative to the melting point would be negligible for these purposes, but if you were to step on ice with boots covered in salt, and push the salt down into the ice... it will melt faster, and increase the surface area of the inner shell, which has nothing to do with the freezing point. The ice is already melting, you're just helping it melt faster by introducing water which has a lower freezing point than the solid you're trying to melt.