Naive question, why is the equivalence relation necessary in the definition of composition of profunctors: http://en.wikipedia.org/wiki/Profunctor. Or if it is not necessary what is the advantage of adding the equivalence relation?

Edited: The remarks on bilinearity, and coherence answered my question. But let's suppose our ctegories are enriched over Vect, I am guess the composition would not be just the tensor product version of the definition, if so why not.