Adaptive optics laser guide-star systems perform atmospheric correction of stellar wavefronts in two parts: stellar tip-tilt and high-spatial-order laser correction. The requirement of a sufficiently bright guide star in the field-of-view to correct tip-tilt limits sky coverage. In this paper, we show an improvement to effective seeing without the need for nearby bright stars, enabling full sky coverage by performing only laser-assisted wavefront correction. We used Robo-AO, the first robotic AO system, to comprehensively demonstrate this laser-only correction. We analyze observations from four years of efficient robotic operation covering 15000 targets and 42000 observations, each realizing different seeing conditions. Using an autoguider (or a post-processing software equivalent) and the laser to improve effective seeing independent of the brightness of a target, Robo-AO observations show a 39% 19% improvement to effective FWHM, without any tip-tilt correction. We also demonstrate that 50% encircled energy performance without tip-tilt correction remains comparable to diffraction-limited, standard Robo-AO performance. Faint-target science programs primarily limited by 50% encircled energy (e.g., those employing integral field spectrographs placed behind the AO system) may see significant benefits to sky coverage from employing laser-only AO.