This is assuming that accuracy depends on the user, rather than the gun.
But we witness the guns autonomously deciding where to aim, rather regardless of where the heroes point the guns - the beams erupt at weird angles to ensure a hit.
If aiming is already just 10% target selection by user and 90% target acquisition by the gun, then it doesn't make much of a difference whether Data or Guinan or Keiko O'Brien wields the gun. An experienced gunslinger (Guinan with her long actual experience, or Data with some downloaded experience) might have a shorter reaction time, though. And the phaser training range seen in TNG seems to be all about target selection and reaction time...