Well not a specialist on tires....but....performance wise a tire has to be a compromise between grip and the longivity! You can build a tire that is very soft but only lasts one lap....or you can build a very hard tire that can last the whole race (if you're not oversteering &/or understeering the car in every corner). A few years ago a Bridgestone engineer said that they once even tried using bugs in the rubber compound to see if it would bring any advantage! (it didn't according to him )
Another thing you have to think about is the tire was....you cannot afford having a flexing tire during corners (a problem that Bridgestone had in 1997 in pre-season testing).....the wall has to be strong enough to withstand the cornering forces!