You're ignoring Alpha Centauri A and B, which are much larger. Also, even without the Alpha Centauri system, very distant orbits (more than 2-3 ly or so) would

You're ignoring Alpha Centauri A and B, which are much larger. Also, even without the Alpha Centauri system, very distant orbits (more than 2-3 ly or so) would be destabilized by the galactic tide, i.e. the gravitational gradient of the Milky Way galaxy.