The benefit of a semiparametric model is that here we are not interested in performing completely nonparametric estimations, where the infinite dimensional parameters might bring intractability.
by considering the semiparametric case, we not only obtain some expressiveness from the nonparametric models, but also reduce the complexity of the task: we are only interested in the finite-dimensional components Σ in the Gaussian copula with O(n log n) complexity, which is not as computationally difficult as the completely nonparametric cases.