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Saying they do not need a number value for a given location does not make it true.No, you do not need to have a number value for the tide at any given time/location. How could you? You can have a number for the sea level at any given time/location, but how do you know what contribution the tide makes to that level, and what is due to other causes? Answer: Fourier analysis. This tells you how much of the level is periodic and how much is due to non-periodic causes.
Again Fourier analysis only corrects for the theoretical sinusoidal functions, if there are other variables, (and there are) then the
correction factor applied is itself incorrect.