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Yup, it's a trade off. Tall sidewalls act like lateral suspension. Having that side-to-side movement does reduce the 'feel' of the car, but usually increases performance when it's boiled down to lap times. (Look at the sidewalls on a formula-one car.) When you have undulating road surfaces with rough spots, dirty spots, oily spots, etc., it's nice to have some degree of lateral flex when cornering. On a perfectly smooth track, this is less important. If you look at drifting competitions, where traction is the enemy, they have as little sidewall as possible, and very wide rims.
Modern racing motorcycles have a certain degree of lateral flexibility in their suspension. When a bike is leaning way over in a sharp corner, a bump in the road surface doesn't move the tire upwards because the suspension is tilted sideways with the leaning bike. Instead, it moves at an angle which really isn't ideal at all. Recently, engineers are building a certain amount of flexibility into motorcycle suspension to allow it to flex sideways to accommodate rough surfaces when cornering. This illustrates the importance of the ability for suspension to move in every direction. Although I've never really read anything about car designers incorporating any advanced lateral flexibility into the suspension of cars, I'm pretty sure they do. The SVX's passive rear steering is a pretty good example of how lateral flexibility can be important.
I prefer big, fat sidewalls. It's not uncommon for racers to replace factory 18's with 17's or even 16's to get those faster lap times. Frequently, the only reason this isn't done because the brakes won't fit inside a smaller wheel.
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