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fact that the cornering or acceleration force that you get with any car is a complex interaction, not one that can be summarized with a few formulas. Some info to consider is that under cornering or acceleration....
- the tire will deflect
- the coefficient of friction will change, tires do not retain a constant coefficient over a range of normal forces, in fact as normal force goes up the coefficient goes down
- during cornering, the loading on the tire probably does not change/increase in a smooth or constant fashion, rather the tire has a spring rate and the normal force at the contact patch probably sees spikes, abrupt changes, etc. I suspect that using a bigger tire is a way to "damp" the effects of any of these types of real world effects. For instance, if you use a small tire, you might see a huge change in available traction as the contact pad deflects, whereas a bigger tires gives less change in traction forces over the range of deflection. It's an interesting question - above thoughts are my opinions only.
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