Ideas about morphological complexity have been used to classify languages and to link complexity to language age and social structure. Creoles and sign languages are often framed as younger and structurally simpler than other languages. Concurrently, sign language morphology has been described as paradoxical, as both simple and complex. This paper is a critical examination of claims about morphological complexity and its relationship to language age and social structure. We show that the theoretical and empirical foundations of claims that sign language morphology is paradoxical are flawed. Specifically, argumentation and evidence supporting analogies between creole and sign language complexity adopt theoretically contested and ideologically problematic assumptions about creoles and uncritically apply them to sign languages. We identify four flaws in argumentation: (i) use of limited morphological data to generate claims about global complexity, (ii) association of binary language categories with categorical complexity differences, (iii) use of language age to motivate predictions about morphological complexity, and (iv) extrapolating from creole complexity to sign language complexity. Based on these flaws, we develop nine theoretical and practical recommendations for working with morphological complexity and discuss uncritical cross-disciplinary transfer of ideas.