Is Dawn dishwashing detergent really superior to other dishwashing detergents?

Always I see tips for cleaning stains and all kinds of stuff, which always specify using Dawn dishwashing detergent.

Yesterday, my hairdresser was telling me that every so often, we should wash our hair with Dawn to clarify it, to get the mineral buildup out. I asked “can it be any detergent or does it have to be Dawn?” and she said “it has to be Dawn.”

Is Dawn dishwashing detergent any better than any other detergent? Is it really better or is it a myth?