Morphological complexity has been used as a measure to classify languages into types that are more and less complex and to link language age and social structure. For example, creoles and sign languages are often framed as young and structurally simpler than other languages. At the same time, some researchers have argued that sign language morphology is paradoxical, describing it as both simple and complex. This paper is a critical examination of 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, the lines of argumentation and evidence behind analogies about 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 anecdotal morphological data to make claims about global complexity, (ii) use of categorical typological groups that reflect colonial ideologies, (iii) false associations between age and complexity, and (iv) a mismatch in morphological metrics used to determine the complexity of creoles and sign languages. Based on these flaws, we develop nine concrete theoretical and practical recommendations for working with morphological complexity and actively engage in dissecting uncritical cross-disciplinary transfer of ideas