If the primary benefit of adding salt was improving thermal coupling through liquid by melting some of ice then you could achieve the same effect by adding some tap water. Which in my opinion would be a lot simpler and less messy than getting salt involved. Some energy would be lost to cool down tap water, but as mentioned in the article phase transition takes a lot more energy than changing temperature of water.
If you had really cold ice cubes, already tightly packed, then the water you add would freeze, making a solid ice sheath around the cream-containing vessel, and yes, that would work great.
But with too much space around the ice cubes, or ice cubes that aren't cold enough, adding water will just give you more cold (but not freezing) water.
I think people have converged on adding salt to ice because it's so forgiving (for a variety of ice cube temperatures and geometries), and the salt itself doesn't appreciably heat anything (unlike your added water). Other comments here quantify this better than I can.
