If it's possible to Shock the fish to death with ice water, which I'm doubtful that it is, Freezing is recognized as an inhumane method by which to euthanize any animals at all.
The "fall asleep and die" bit is fiction.
As the animal freezes the water in the cell walls expands and causes the cell walls to rupture and is extrapolated by tests on various animals to be EXTREMELY painful and a freezing to death a horribly inhumane procedure.
The real reason people like is the "out of sight, out of mind" ease and the lack of the feeling of "active participation that come with some of the more human, less "hands off" dispatch of the animal in question.