The point of my explanation is to point out that freezing the fish quickly and solidly is the motivating reason behind using salt. OP's question is ignored here because it's not relevant and because OP came right out and said they didn't understand.

But I'll repeat the parts you seem to have missed too: The goal is to rapidly transfer a great deal of heat away from the fish. Not just quickly but also to a lower temperature.

In this system, you want to declare the marginal difference of having an internal layer of air immediately adjacent to an insulating material as a defect... but it's simultaneously an advantage with respect to the fish which is not insulated. There's a minor trade off here at best.

The heat debt from the phase change if done using sufficient quantities of ice and salt is overwhelmingly sufficient to fully freeze the fish and keep it frozen for the period of transportation. The marginal loss of heat through the insulated walls of the cooler is small enough to be considered irrelevant.