In addition to the answer by @issoloroap, the article Prolongation structures of nonlinear evolution equations by Allan Fordy (here is the Mathscinet link and here is its first page on Google books) explains why "good" zero-curvature representations should live in (semi)simple Lie algebras.
Another important point is that the spectral parameter should be essential, i.e., it should not be removable by gauge transformations, cf. e.g. this paper and references therein, and for the discussion of related issues in the case of dispersionless sysems in more than two independent variables see e.g. this article, and this one, and references therein.