A stiffer suspension is faster weight transfer, actually called load transfer since, like a go-kart, it's not very much due to body roll. And then faster load transfer is more traction on the turn-in. The problem is, how fast of a responding vehicle can the driver or rider handle ?

Also, faster load transfer works the tires harder and therefor the setup for a low-traction surface is a softer suspension.

The other subject was "Turn left". Well, turn-left is okay but steering is really a leveraging of the tire against the track. Then the contact-patch deflects out-of-line from the tire. As long as the contact-patch can further deflect then there is traction. The path of the vehicle is the result of the leveraging of the tires against the track but since both the front tires and the rear tires have contact-patch deflection then there is tire drift at both the front and rear such that there is not much apparent steering angle at the front wheels. The contact-patch deflection is called "slip angle" but really should be called drift-angle. Oh, on a four-wheel vehicle it's the outside tires with load on them that have significant slip-angle and drift in a curve. Note that the driver or rider doesn't steer through a curve under g-forces but just experiences the natural path of the vehicle due to the leveraging of tire force !

Now, for instance, the sport of "drifting" is really a sport of power-sliding because the rear tires are overloaded and can no longer further deflect the contact-patch. That's a slide.