As sidewalk delivery robots become increasingly integrated into urban life, this paper begins with a critical provocation: Is robot labor labor? More than a rhetorical question, this inquiry invites closer attention to the social and political arrangements that robot labor entails. Drawing on ethnographic fieldwork across two smart-city districts in Seoul, we examine how delivery robot labor is collectively sustained. While robotic actions are often framed as autonomous and efficient, we show that each successful delivery is in fact a distributed sociotechnical achievement--reliant on human labor, regulatory coordination, and social accommodations. We argue that delivery robots do not replace labor but reconfigure it--rendering some forms more visible (robotic performance) while obscuring others (human and institutional support). Unlike industrial robots, delivery robots operate in shared public space, engage everyday passersby, and are embedded in policy and progress narratives. In these spaces, we identify "robot privilege"--humans routinely yielding to robots--and distinct perceptions between casual observers ("cute") and everyday coexisters ("admirable"). We contribute a conceptual reframing of robot labor as a collective assemblage, empirical insights into South Korea's smart-city automation, and a call for HRI to engage more deeply with labor and spatial politics to better theorize public-facing robots.