Hot luminous stars are characterized by their fast, dense and persistent outflows. Here, we analyze the unambiguous spectroscopic signatures of the presence of these winds. We then present various observational elements that suggest that hot star winds are not smoothly expanding outflows. The unstable nature of line-driving could be at the origin of these properties of radiatively-driven outflows and we investigate here its ability to explain the Line Profile Variability (LPV) observed in hot star spectra. Such variability features profile sub-peaks migrating away from line center, and with characteristic velocity scales increasing from 50 to 100-200 km s-1 (from center to edge). Based on radiation-hydrodynamics simulations, we compute the average and temporal evolution of the emissivity of a hot star wind, and compare with LPV datasets of Wolf-Rayet (WR) spectra. The inferred inadequacy of the spherically-symmetric assumption suggests a globally asymmetrical wind structure, which we model by mapping the 3D wind volume with closely-packed star-centered cones. We find that the cone-angle α, which represents the lateral extent of wind structures, controls the sub-peak width at line center. Given the absence of an explicit lateral velocity in our simulations, the best match to observations suggest an upper limit of ca. 1-3 deg to these structures. At line edge, synthetic sub-peaks are narrower than observed by a factor 2-3, suggesting the lack of radial velocity dispersion of computed wind structures, a likely artifact of our 1D simulations. Additionally, assuming that sub-peak lifetimes in LPV time-series represents the crossing-time of the Line Emission Region (LER), we determine the wind acceleration in the LER. Contrary to previous findings, we find no firm evidence for very extended acceleration of WR winds, which would require using spectral diagnostics with LER located distinctly below v∞. Although the best candidates, WR objects and their optically thick outflows constitute a big challenge for constraining observationally the velocity law of radiatively-driven winds.