Doing something wrong for a long time doesn't make it right, no matter how long you've been doing it wrong.
Admitting you can't tell the difference in performance is just an admission that you've either never been anywhere near the limits of those tires or that you don't know what a good set of tires is actually capable of. It doesn't prove there isn't a difference.
All it takes is a couple laps at an autox or road course. Take a couple laps with tires that are on too narrow a rim, then swap them out for tires that are properly sized and take a couple laps. I've done it, the difference is obvious. Just like how adding or dropping a few psi in your tires can dramatically change your traction, lap times, or ET's at the strip. There's a range of tolerances for that too, doesn't mean you can't do it wrong. You can learn more in those few laps about how those tires work and how your car handles than you'd ever learn driving on the street in normal conditions.
No, you won't notice it driving back and forth to the Dairy Queen or the cruising to the local show in the slow lane on the weekend when the weather is nice. You could drive for decades or tens of thousands of miles on the street and never notice. But when the crap hits the fan and you need that extra performance to avoid an accident, it won't be there. And you won't even know any better, because you've never done it any other way.