depending on how the car is setup, an air filter will make some run faster..Yup. I have never heard of ANY street engine not having a good filter. Racing (strip) enigines don't need one as you are not putting any miles on the motor at all, even after a few years of use. Now in cold winter air, you do not need a filter as the snowmobile companies have run tests, and there is so little particulate (dust etc.) in the air it really doesn't matter, but that is an extreme exception.
The air filter "cleans" up the air flow (turbulent to laminar), not just the air from particulates..
a carb exposed to the direct air flow can do a lot of stupid stuff from disturbed air. Turbulent air down the top of a carb just does not work as well.. not such a big deal on and FI motor..