If anyone is really interested;
However a rubber type is a lot softer than metal, and a road is a lot rougher than a metal plate. Even at low loads the tyre deforms to key into the irregularities in the road, so increasing the load has a lesser effect. That's why you get the sub-linear dependance described in the Wikipedia article.
And anyway, if by "grip" you mean grip when cornering, the grip isn't just controlled by the contact patch area.
...the reason why wider tires are chosen is because they last longer than thin ones!
Italics cos it’s quoted from a couple of sources and not my original words.
https://en.m.wikipedia.org/wiki/Tyre_load_sensitivity