Frictional sliding is an intrinsically complex phenomenon, emerging from the interplay between driving forces, elasto-frictional instabilities, interfacial nonlinearity and dissipation, material inertia and bulk geometry. We show that homogeneous rate-and-state dependent frictional systems, driven at a prescribed boundary velocity — as opposed to a prescribed stress — in a range where the frictional interface is rate-weakening, generically host self-healing slip pulses, a sliding mode not yet fully understood. Such velocity-driven frictional systems are then shown to exhibit coarsening dynamics saturated at the system length in the sliding direction, independently of the system’s height, leading to steadily propagating pulses. The latter may be viewed as a propagating phase-separated state, where slip and stick characterize the two phases. While the coarsening process is limited by the system’s length — leading in the presence of periodic boundary conditions to a pulse train with periodicity identical to the system’s length —, the single pulse width, characteristic slip velocity and propagation speed exhibit rich properties, which are comprehensively understood using theory and extensive numerics. Finally, we show that for sufficiently small system heights, the pulse is accompanied by periodic elasto-frictional instabilities.