Are there any RWYB Wheel to Wheel road races?
 

Is there a "Run what you brought" style road races that are wheel to wheel? I know there's time attacks but what about wheel to wheel racing?

Time attacks only if you mean an uncaged car.

If you have a race car (legal with some sanctioning body like scca, NASA, pca, etc) then you can run chump car EC class for fun.

You should never do w2w racing unless you can afford to push the car off a cliff and walk away.