Traffic flow is a function of many natural, environmental, and human factors. Not only that weather and road condition can vary, but drivers' decisions and policies also can affect the flow. Here we analyze the effect of distribution of desired speeds. We show that a broader distribution can reduce the flow efficiency and increase congestions. Since different drivers react differently to changes in weather or road conditions, such a change leads to a change in desired speed distribution as well. As a result, nonintuitive changes in traffic flow may occur. Besides providing insight and analyzing the underlying mechanism of a collective phenomenon, this example sheds light on a fundamental aspect of computational modeling. Although "mean-field" models that deal with average values only and ignore variability are simpler and easier to analyze, they can very easily turn into oversimplifications and miss relevant qualitative phenomena.