It is possible to over do it. Low stiff sidewalls don’t conform to bumpy surfaces easily. This makes ultra low profile tires sensitive to shock, as the super short, stiff sidewalls have very little compliance. Harsh surface inputs can make these tires skip and hop across the surface instead of digging in and finding grip making ultra low profile tires more sensitive to shock tuning. Big wheels are heavy creating a flywheel effect which is harder to accelerate and brake. Huge dubs also screw up your gear ratio contributing to sluggish acceleration.
Lastly, big heavy wheels and tires also add unsprung weight which reduces the effectiveness of the suspension. Unsprung weight is the weight of the components that are not suspended on a car. This includes the suspension arms, brakes, half of the shock absorber and the wheel and tire. Typically unsprung weight is 12-15% of the total weight of a car. For the suspension to work well, the ratio of sprung to unsprung weight must be kept as low as possible. For instance, have you ever noticed that the suspension of monster trucks hardly works? Even though they may have wheel travel measured in feet instead of inches, it’s hardly ever used and the trucks bounce and bang around like crazed Tonka toys. This is because Monster Trucks have a very high ratio of sprung to unsprung weight. Those huge earthmover tires possibly weigh more than the whole truck. When surface irregularities are hit, high unsprung weight generates significant force with an upward component which means a rough ride and difficulty keeping the rubber on the road. High unsprung weight means that the shocks have to work much harder to damp wheel movement as well. Reducing the unsprung weight and the suspension is worked less, the ride improves and the tire can be kept in contact with the ground better.
For these reasons, putting a 215/35-18 on the same compact FWD car that worked well with a 205/50-15 will probably reduce its performance. Doing something really dumb like putting a 245/25-22 on an EVO is very detrimental to performance.
Generally for small bore naturally aspirated 4-cylinder like the older Honda Civics and Nisan Sentras, a lightweight 15×7″ wheel is the best bet for performance. For larger cars about 18″ is the usual practical maximum wheel diameter. Larger than this, you won’t find as many choices in sizes for true high performance tires. Wheels larger than 18″ in diameter are mostly for show except in a few cases like the R35 GT-R which needs its big 20″ wheels to clear its huge 15″ brakes. Dub sizes don’t have ultra high performance applications either; the huge, oversized in diameter tires offered are mostly designed for the NBA player or gangsta rapper aesthetic.