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.
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.