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We investigate the presence of hub-filament systems in a large sample of 146 active proto-clusters, using (HCO+)-C-13 J = 1-0 molecular line data obtained from the ATOMS survey. We find that filaments are ubiquitous in proto-clusters, and hub-filament systems are very common from dense core scales (similar to 0.1 pc) to clump/cloud scales (similar to 1-10 pc). The proportion of proto-clusters containing hub-filament systems decreases with increasing dust temperature (T-d) and luminosity-to-mass ratios (L/M) of clumps, indicating that stellar feedback from H ii regions gradually destroys the hub-filament systems as proto-clusters evolve. Clear velocity gradients are seen along the longest filaments with a mean velocity gradient of 8.71 km s(-1) pc(-1) and a median velocity gradient of 5.54 km s(-1) pc(-1). We find that velocity gradients are small for filament lengths larger than similar to 1 pc, probably hinting at the existence of inertial inflows, although we cannot determine whether the latter are driven by large-scale turbulence or large-scale gravitational contraction. In contrast, velocity gradients below similar to 1 pc dramatically increase as filament lengths decrease, indicating that the gravity of the hubs or cores starts to dominate gas infall at small scales. We suggest that self-similar hub-filament systems and filamentary accretion at all scales may play a key role in high-mass star formation.