Robots in homes must continuously sense the people around them, yet most prior work relies on limited or offline perception. We argue that perception quality is the dominant factor governing what interaction is achievable at home, and build a testbed to test this claim. OmniRobotHome instruments a furnished home with 48 hardware-synchronized cameras and three manipulators in a unified world frame, delivering real-time markerless full-body human pose, 6D object pose, anticipatory motion forecasting, and a social avatar agent that converses with residents. Using the platform, we treat perception quality as an experimental variable across safety, human assistance, and social interaction, and find that interaction quality degrades measurably as real-timeness, granularity, coverage, accuracy, forecasting, or memory is weakened. All code and data will be released.