Arad (2003, 2005) has argued that syntactic composition begins with category-neutral roots rather than larger, already-categorized atoms like verbs and nouns. The argument was based on asymmetries reportedly observed in both English and Hebrew: a single root may acquire an idiosyncratic meaning or pronunciation up to the level of the first category-assigning head, but later morphology is semantically and phonologically predictable. This asymmetry was argued to suggest a locality constraint applying below the word level which would follow from independent syntactic constraints on the assumption that roots merge in the syntax. In this paper, we re-evaluate Arad's evidence for these asymmetries. We show that upon a closer look at the Hebrew and English facts, the predicted correlation between attachment height and semantic or phonological predictability is not observed. This undermines both the original argument for the syntactic reality of category-neutral roots and its consequences for our understanding of locality restrictions on semantic and phonological interpretation.