A tire brush will not clean the entire side of a tire, anyway. If you think of the sidewall as from where it meets the wheel, to where it meets the ground - the curvature of the sidewall and the fact that the tire brush itself is round - at best you'll only cover the middle third or maybe half of the entire sidewall - even less for larger tires. As Earl said - it will take care of a whitewall, or raised lettering, which is generally in that middle portion of the sidewall.
If you want to clean the tire - make the black look blacker/cleaner, you need a tire cleaning chemical (one that allows you to actually see the dirt lifting off the tire when it is sprayed on) and some type of wheel or lower detail brush that has a large diameter - filament or foam - that will actually reach the span of the entire sidewall - wheel to ground. A brush with a large enough diameter will work on the wheels and if large enough - assist with rockers too - you'll get more cleaning than just the tire out of it.
I just don't see too many tire brushes anymore - I don't have any.