Didn't they sweep with their hand phasers in "The Arsenal of Freedom"?
They did. They also missed their target quite a few times, though not for lack of trying.
I don't really have a problem with a moving conduit myself. If the conduit propagates at the speed of light, the beam will sweep like an ordinary laser pointer. Whether the actual weapon fires in pulses or beams, the CONDUIT can move anywhere you want it to.