Why would nonlinear generalizations be an issue? Wouldn't adding some constraints get us Maxwell's Equations? It seems significant that this can be done at all

Why would nonlinear generalizations be an issue? Wouldn't adding some constraints get us Maxwell's Equations? It seems significant that this can be done at all even if its not complete but maybe I'm missing something. It reminds me of Einstein's original geometrization, possibly even a breakthrough if it turns out to have uses in further development of theory.