Except for electric cars. They suffer because the battery is not able to make the sustained output necessary to provide full acceleration for that amount of time. However, it says absolutely nothing about the tires, suspension and braking. I don't care just about 0-60 times, handling is extremely important to me because I drive a windy mountain road every day. However, I find track times to be a lousy way to compare handling performance between a BMW and Tesla for the above reason (I might drive the road at 60 mph, not two or three times that). Also, acceleration responsiveness is very important to me, and there my current Tesla is far better than my old BMW (I need to quickly overtake a car going uphill and don't need to downshift or wait for a turbo to spool up). I eagerly await results on Model 3 handling.
In summary, 0-60 times are not the be all and end all of performance measurements, but neither are track times.