The F1 of the 70ies car have those balloon tires cause of the FISA(FIA) rules: only 13" rims were allowed, if remember correct, and yes those tyres done a lot of suspension work, they had a big and soft shoulder.
For radials with diameter and their height stiffness there is a simple rule: each mm you make the shoulder smaller in height, you haye to increase their stiffness.
And those tyre types have one major difference: their inner nylon belts and how they lay in the rubber. In diagonals the layers are - diagonal. A diagonal tyre had advantages in curves, when tires are small in width. So motorcycles had them up to the mid eighties.
Radial tyres have their layers in radial direction, often accompanied by some steel rings(steel belt). Radials can take much mor forces in the cars driving direction( so they let you accelerate and brake better) but they are bad in taking side forces, when their shoulder is high and soft.
Tire pressure is an easy way to make an axle stiffer or softer, within the tyres limitations.
Too low pressure will cause overheating, slows down the reaction of the car, increase massivly the wear at inner and outer tire side and can cause it to explode.. bad thing when you drive 350 in a 917 in Le Mans.... in RL you had good chance to be get killed...
Too high pressure causes faster reactions of the car, makes it more bumpy and increases the tire wear in the middle of the tyre.
The prototypes, GT and touring cars - especially for endurance racing pushed the tyre manufacturers more in the evolution, which benefits we are all appreciate when we drive our daily driver. Just compare the rims and tires of an 906 up to the 908 and then 917 and so on. The rims seem to explode in diameter and width and the tyres smaller in their diameter height, radials helped to make them stiff enough to take the brutal forces, but the cars suspension has much more work on bumps and to keep the car on the road.
And then keep in mind what the poor rear tyres of an 917/30 had to endure... up to 1500 hp released on them... and those terryfing curve speeds in the bankings... i´m still surprised how mid 70ies tyres can take this... but they did.