When I rode my Sears garden tractor (those have lower-profile tires) for the first time, it felt like go-karting on an abandoned log road. It turns out that there was 17psi in all 4 tires, while the markings specified 10 and 12 psi. The tires were sitting on the pavement perfectly round, and the contact patch must have been about 3" by 3".
On relatively hard surfaces like mature lawn, the grip is directly related to the contact patch. After I dropped the pressure to 8 psi (I like a comfy ride but not a flat beer) the contact patch looked like it more than doubled. Although I did not have grip problems, that would certainly have helped.
In another post I described the excessive toe-in my front wheels showed when I got the tractor. We're talking 3.2 degrees. You need to hit an SUV with your car to get that kind of toe-in on it. Although there are opinions that toe-in helps steering response in turns, I doubt it is intentional because of the cost in straight line stability. If toe-in really helped, the technique would be used in car racing (although they do use skewed camber and caster adjustments).
The wheel spindles geometry already takes care of turning the inside wheel by a greater angle than the outside wheel, so each gets its own turning radius for maximum grip. These angles are carefully calculated based on parallel position at 0 degrees and are a function of the track and wheelbase. Any toe-in or out throws off the two turning circles for less optimal grip.