You seem to have the best of two worlds.
If the jaws can be individually adjusted, it can centre work as accurately as you want, provided that you have the equipment, time and motivation.
I wouldn’t be without my four jaw independent chucks.
Not used all the time, but necessary for accurately centred, eccentric, or non round work
For most work, 0.0005″ (0.012 mm) will suffice for my work.
Howard