Chris King Headset. Just wondering how sensitive these are to accurate SFN positioning ? & wonky steerer cutting ?

On the bike it appears to have some play in the bottom race, however with the bits in hand its fine (as far as I can tell). Only thing that seems to alleviate the play is over-tightening the headset cap. (Leading to premature bearing wear I would imagine). I’m thinking maybe the overtightening is pulling the SFN straight.
These SFN insertion tools, do they need a nicely cut steerer ?
This aside it is incredibly smooth.