Well, I don't want to go into too much detail because I'd have to explain the culture behind tire stretching(hipari), but without much explanation I'm sure it's not hard to believe that it significantly reduces side-wall flex. Because of this there's a better feel for the car's behavior and in some cases, a car can exhibit better turn-in. Not only that, but I've read in many cases where theoretically, stretching can provide somewhat of a static camber for a solid rear-axle vehicle. I've done my share of experimenting, and I saw the biggest benefits when I had to run a cheaper tire with a larger sidewall. There is a fine point where stretching too much has absolutely no gain, but minimal stretch can be beneficial in some cases.
Obviously you're going to want the largest contact patch possible for best grip, but if you're doing mega stretch on a rim just because you want a huge rim to fit a car, there's absolutely no benefit. I'm no expert however, I'm just going by what testing I've seen done by Formula D, D1GP, TRD developers and other experienced drivers, and even my own personal experience with what tracktime I do have under my belt.