Low profile tires will give a better initial turn-in feel. There is less rubber to stretch and wiggle sideways when you turn the wheels. Call it turn-in "lag"... Softer winter tires sometimes give that type of mushy feel too. Now if you put on sport tires, even with some sidewall they'll be stiff enough to be okay for most people. That's what I do. Whether that's "useful" on the street is arguable and is a personal thing. You can go to the other extreme and drive an SUV that has huge tires but small wheels, if such a thing still exists. Many years ago I had 16" wheels on a Mitsubishi Outlander with huge sidewalls and you could feel it when turning the wheels at speed.