I think one has to understand structuralism to see what it is that the postmodernists are deconstructing. It's not so much that structuralism is the forerunner of postmodernism; it's rather that postmodernism (and its cousin, poststructuralism; many postmodernists are poststructuralists) is a reaction against structuralism and makes a lot more sense with structuralism already in mind.
I see your point and I definitely agree. Do you think it is necessary to have a balanced understanding between both camps? Or does it suffice to be merely proficient in one?
A final question: do advancements in linguistics/other fields that step beyond or displace the ideas of Saussure necessitate a disagreement with postmodernism? Can/has postmodern thought been updated to some of the more modern ideas of the likes of Chomsky/Pinker, or are the deconstructions, borrowings, and appropriations of postmodernism frozen in its own moment of conception?