In historical foundation of Newman-Penrose (spin-coefficient) formalism, the underlying motivation for the choice of a null basis was Penrose's strong belief that the essential element of a space-time is its light-cone structure. I'm still seeing light-cone as just a constraints on velocity!
How penrose see light-cone as the most fundamental entities that can be used to describe the structure of spacetime??
Two Lorentzian scalar products in a vector space have the same light cone if and only if the two scalar products are proportional (one is a constant --- WLOG positive --- multiple of the other). Since causality is determined by the light cone (i.e. future/past), then the causality of a spacetime $(M,g)$ depends not really on $g$ itself, but on the conformal class of $g$.