The development of reliable assistive devices for patients that suffer from motor impairments following central nervous system lesions remains a major challenge in the field of non-invasive Brain-Computer Interfaces (BCIs). These approaches are predominated by electroencephalography and rely on advanced signal processing and machine learning methods to extract neural correlates of motor activity. However, despite tremendous and still ongoing efforts, their value as effective clinical tools remains limited. We advocate that a rather overlooked research avenue lies in efforts to question neurophysiological markers traditionally targeted in non-invasive motor BCIs. We propose an alternative approach grounded by recent fundamental advances in non-invasive neurophysiology, specifically subject-specific feature extraction of sensorimotor bursts of activity recorded via (possibly magnetoencephalography-optimized) electroencephalography. This path holds promise in overcoming a significant proportion of existing limitations, and could foster the wider adoption of online BCIs in rehabilitation protocols.