Autocross/Road Course driving on 15" wheels. What's your experience?
IMO the first consideration when changing sizes is to check the load rating.
Using shorter tires for competition drops the CG and roll centers while also improving the gearing when the car is not a dedicated competition vehicle.
Very hard to judge visuals based on track photos, especially autocross. Bodies move around alot. Heck, everything moves around a lot. LOL. Look at the tires - especially the Hoosiers. Even rims flex a little, especially spun and stamped ones. When Scott Harvey recommended doubling up on the wheel spiders, he knew what he was talking about - and that was for rally's with tire technology 50 years ago!
Same wheels and tires as top photo, hitting the brakes after the finish - and this was a run in the damp. See how much room appears over rear tires. LOL
I was looking for a pic of modern 'vette in the 180 but 'stang entering the same turnaround will do as an example.