Inflating the tyres has 2 reasons. It stops the car having too much grip, which means it will let go at much lower speeds, but also in the high speed turns, it stops the sidewall from potentially folding under the rim which would in turn ram the rim into the floor And actually, when I pumped mine up to the max, the Falkens were still rolling over quite a lot and getting quite near the wear triangles on the sidewalls.
So in my opinion pump them up to around 5PSI shy of the max rated pressure (a little lower to allow for them heating up)