Tire pressure question

Exactly. Race cars are not street cars. Low pressures spell doom in cornering where it might be desirable in straight line acceleration. Higher pressures give the tires stiffer slip angles which are more desired in cornering...
Another consideration for road racing is what happens if you have an off track event. With soft tires and sliding sideways, if you hit a bump or hole you could break the bead loose and lose all your tire pressure. The rim digs into the dirt and over you go.
Hard tires do not flex and heat up as much.