The tire is the most important part of any race car. Running taller than stock tires is.... unusual, often detrimental. We usually advise racers to run enough tire height to not alter ride height / ground clearance on its own dramatically (within 1-2" of stock height, usually shorter) while keeping "enough" sidewall, and maximizing width above all else. The reality of the performance tire world is that there aren't a lot of options in the right tires above 27" in total height.
The stock S197 tires in the 27.0-27.25" height range limit you to very few "good" options outside of the drag racing world. Using tire height to "fix" gearing problems is a "low reward" end game. Changing final drive ratio is painfully easy and inexpensive in the S197 8.8" rear end, especially compared to some other markets. That image above shows a 255/40/19 OEM 2011 GT tire next to a 285/30/18... which is 24.8" tall.
MASSIVE difference in height, and the 285/30/18 is popular on a lot of other cars, but looks ridokulous on the S197, even after being lower 3" in ride height on proper coilovers.
For BMWs like this E92 M3 above you have as few as 3 gearing options, and they are all $1200+ for the ring and pinion alone. For the EVO X next to it the choices are even worse. But for the Ford 8.8" 28-31 spline axles that come in the S197 chassis you can get proper Ford Racing gearing options in dozens of ratios for under $200 in parts. Its about 2.5 hours of work by a properly qualified shop, so its relatively CHEAP compared to many other cars.
Taller tires add more mass - which has to be sped up and slowed down, turned and damped, and the sidewall acts as a spring, too. But I'm not one for ultra-low profile sidewalls, either. There has to be balance in sidewall height, total tire height, wheel diameter (just enough to clear the brake rotor/caliper), and
tire availability.
That last bit above is the key element that drives many builds: what sizes are available that fit the class/car/weight/power. We often look at a chassis, figure out what class we want to build for, then find the ideal tire for the car/chassis... and
build the entire car around this tire. We have done that many, many times. Why?
Because the tire is the most important part of any race car.