IMO there is no difference in turning only left or both left and right as to what needs to happen in a kart.
the rear inside wheel must lift…or unload (sometimes just skimming the ground is enough) in order to turn a kart with a solid live axle effectively…to maximize the speed through the corner.
as for the control….i agree that it can control it…but in a kart…the “jacking” (front spindle) is not the only thing accomplishing the ability for the kart to turn…control it.
if that were the case….we would tune the whole kart with only one tuning input.
from racing on the dirt in a minisprint i have learned that the “timing” is the shock. how quickly the left rear compresses and then how quickly…or slowly it rebounds. more grip or a larger radius corner and the timing of the rebound must be slowed down.
in a kart you accomplish that with …axle…hubs…seat struts etc.
but in a LTO kart you preload…or unload the corners with the jacking adjustment…since you are only an LTO mode. so maybe concentrating on that adjustment is the key in an Lto dirt …asphalt kart…i dont know…never raced a kart on the dirt or on an oval.