Neural populations synchronise their activity with either zero-phase delay (activity in interacting regions occurs simultaneously) or a phase delay (activity in one region follows the other). In electroencephalography and magnetoencephalography functional connectivity analyses, artefactual connectivity can also occur with zero-phase delay. To minimise artefact, contemporary analyses typically exclude all zero-phase-delay interactions. However, the extent to which "true" interactions are resultingly lost-and the impact this has on the performance of functional connectivity metrics as biomarkers-remains unknown. Here, we show that most cortico-cortical functional connectivity occurs with zero- or near-zero phase delay, even where such connectivity is unlikely to be artefactual. Including, rather than excluding, zero-phase-delay connectivity increases the reliability, convergence with neurobiology (structure-function concordance, homotopic interhemispheric connectivity, and age-related connectivity changes), and prognostic ability of functional connectivity metrics. We find that excluding zero-phase-delay connections penalises functional connectivity strength between the strongest structurally connected regions: stronger structural connections lead to functional connections with phase delays closer to zero, mediated by a shorter signal propagation time. Our findings challenge generally accepted assumptions that zero-phase-exclusive methods are superior to zero-phase-inclusive methods.