Highly regular laser-induced periodic surface structures (HR-LIPSS) have been fabricated on surfaces of Mo, steel alloy and Ti at a record processing speed on large areas and with a record regularity in the obtained sub-wavelength structures. The physical mechanisms governing LIPSS regularity are identified and linked with the decay length (i.e. the mean free path) of the excited surface electromagnetic waves (SEWs). The dispersion of the LIPSS orientation angle well correlates with the SEWs decay length: the shorter this length, the more regular are the LIPSS. A material dependent criterion for obtaining HR-LIPSS is proposed for a large variety of metallic materials. It has been found that decreasing the spot size close to the SEW decay length is a key for covering several cm2 of material surface by HR-LIPSS in a few seconds. Theoretical predictions suggest that reducing the laser wavelength can provide the possibility of HR-LIPSS production on principally any metal. This new achievement in the unprecedented level of control over the laser-induced periodic structure formation makes this laser-writing technology to be flexible, robust and, hence, highly competitive for advanced industrial applications based on surface nanostructuring.