In performance circles, the tire sidewall is considered to be a part of the suspension. The flexible sidewall acts exactly like a spring. So in effect it's an extra spring in the suspension system. If you have a very rigid sidewall, then it makes your suspension stiffer. If you have a "bubbly assed" sidewall then your car will behave as if there is an undamped spring in the system. I think this *would* affect the handling of the car, but would it affect the handling of the tire? I don't know.
If you lose all the air in a run-flat, sure you can keep going at 55, but that doesn't mean you can run the slalom in one with equivalent performance.
Calvin