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Just my experience.
The times I've used shampoo the least frequently have been when surfing / diving. It quickly became a matted sticky mess. Water didn't change that.
That said I probably didn't have access to a decent quantity of properly hot water, so maybe that plus short hair would have made a difference.
Also I don't agree that sea water is just salt + water. It totally depends where you are but sand, shit, ground plastic and plant matter are generally also present.
sea water is just salt and water, it isn't some miraculous chemical soup*
as we all should know, salt is dissolved by water, more so by hot water, so why wouldn't a shower work to rinse the sea out
*unless you are swimming in a non blue flagged beach and have been bumping into dogs / human eggs and general effluent