Had an old Saturn buddy with 35s on his Saturn. Flying around a corner, the tire rolled and touched the rim to the road... The car slid across the road and down a hill taking out an on coming car in the proccess.

If you want to do lapping you want a stiff sidewall. My R-Comps have a sidewall stiffer than a concrete wall (exaggeration, but not much). Soft sidewall tires are terrible when you're pushing a car hard or especially at its limit cause you just scrub the sides of the tires, will cause damage to the tires and can even de-bead a tire.

Tires are unpredictable. Suspension is predictable. You want as much force transmitted to the suspension as possible (ie as little tire flex/roll/deflection as possible).

Lapping and soft sidewall tires do not go together. Water and oil.