If the rules allowed - a low profile tyre would let you run bigger brake discs for a given rolling radius.
I won't give you BS about stiffer sidewalls etc. - I'd just be guessing! But at a GUESS
it's probably easier to control the sidewall flex. Certainly if you drive a car with low profiles they feel more direct (also tend to break away more suddenly).
I am pretty sure that the low profile tyre weighs less (less of it - so surely?) - and the extra wheel does not weigh that much more. So you have benefits with unsprung weight and intertia.
Having low profiles has to be an advantage with the suspension design. At the moment some of the car's spring is in the tyre (probably much more than they would like). They don't have much control over it's rate or damping. Putting low profiles on must give back some control of the car's springing and damping to the stuff in the chassis that was actually designed for the job in the first place.