Doesn't a larger tire mean a larger contact patch on the road? So perhaps a little more mechanical grip to aid with the loss of aero downforce?
No not really geet. the contact area is very funny thing and the fact that rubber behaves weird by science standards, it it far more complicated than that. When all you do is widen the tire the actual contact patch gets wider but it also shortens front to rear. Where the benefits of a smaller profile tire come in is in being able to have less rubber on the sidewalls, which therefore increase feedback and reduce flexing/rolling etc. So much more of the energy can go toward the actual contact patch. The compound of a tire can increase the friction by tenfold of the energy you put into it. So when you brake it's the tires that are stopping you, when you accelerate it's the tires that are accelerating you. That's why all modern road racing cars use low profile tires, they're just quicker and more efficient at transferring the energy both to stop and to go.
The only drawback to a larger combination comes from the fact that you have to have a larger rim, therefore more weight and more rotational mass, but it's not a factor in F1 where they're already using exotic materials for the rims. (it used to be a magnesium alloy) although I don't even know if that's ever the current metal in use. In every other aspect it's a win, and that's why you see that as the standard in LM and other series.