You would need two because we have both left and right turns, so the differential may apply to either wheel.
If you only apply it to one wheel, the one can only get a different speed in one direction. These are freewheel or overrun clutches, not differential gearboxes.
Currently the speed differential is about 1 revolution for every 80 degrees of turn.(360/4.6),
ie: the outer wheel turns 4.6 turns more than the inner wheel for every 360 circle.
Karts currently drive the outer wheel because centripetal force tends to lift the inner wheel.
With an overrun clutch, one would drive the inner wheel and the outer wheel would overrun. We can see that this would mean significant differences in the way we drove and designed karts, trying to keep the inner wheel on the ground in the corner.
Just having an over run clutch on one wheel would mean that when turning in one direction one would keep the inner wheel on the ground, and turning the other you would have to lift the inner wheel.
Looks like more problems than it solves.
Of course, if you are always turning in one direction, then design the kart with negative jacking on the front to load the inside wheel and fit a single overrun clutch on the outer wheel.
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