You have two or three sometimes opposed elements at play here.
1) The responsiveness of the system - this is how quickly it reacts to inputs. This is largely dictated by stiffness.
2) The balance of the system - essentially, stable or unstable.
3) The performance of the system - this is the max forces/loads the system can respond to.
For number 1, the stiffer the system, the faster it responds to inputs. The more closely mass is distributed with respect to the centre of gravity, the faster it responds to inputs.
For number 2, unstable systems respond to inputs more quickly than stable ones (see modern fighter jets as an example). In karts, this can be encouraged by having an oversteer balance, using toe out, increasing caster etc.
For number 3, this is largely dictated by 1 & 2 above. As an example, think of driving in the wet and how the kart understeers. Whilst you set the kart up to change direction quickly, it is still reluctant to change direction.
I've found going narrow at the front makes the kart pointy, but more prone to understeer. Going narrow at the rear makes the kart pointy, more prone to oversteer in the fast stuff and understeer off the slow stuff. Toe out always makes the kart pointy at the cost of straight line speed and increased front tyre temps. Raising the CoG will make the kart change direction less quickly but with greater magnitude (the "greater magnitude" bit can often make the kart feel like it changes direction better).
Having said all that, poor direction changes and a difficult to place kart is the major symptom of a worn out chassis. A new chassis is considerably easier to drive, but not necessarily that much quicker.
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