We present a phenomenological theory of the interplay between linear self-assembly, isotropic attractions, and orientation-dependent repulsions in determining the phase behavior of particles that reversibly polymerize into semiflexible chains. Important examples of such linearly aggregating systems include many proteins, micelles, and dipolar fluids. Four classes of phase diagrams are predicted, featuring coexistence regions between two isotropic phases, an isotropic and a nematic phase, or two nematic phases. We map out the evolution of phase diagrams with changing values of the chain persistence length and of the ratio of intrachain bond energy to isotropic attractive energy, and relate the behavior in equilibrium polymer systems to that of fixed-length polymer systems. In both cases our theory predicts that over a narrow range of persistence lengths, increasing the chain length leads first to the disappearance and then to the recovery of the isotropic-isotropic transition; this behavior is explained by a simple scaling argument.