Seems like the right moment in time to legislate a maximum acceleration for street legal cars.
There are a couple of good videos of Model S doing launch control on YouTube: https://youtu.be/8I-6_H0haAw?t=248
If one can afford a Model S, one can afford a lawyer to ask the judge for the court's accepted definition for "display of speed". My money says a Tesla with pedal mashed and launch control on would not fit the definition. All one is left with is pulling an illegal number of Gs, which I don't think cops have a measuring gun for yet.
In the real world, I've launched plenty hard on motorcycles on a regular basis to this day, and have occasionally blown past a sitting cop while doing it (getting around traffic from a light, or what have you). No smoke from the rear tire, front wheel stayed on the ground, speed not exceeded (or not by much), I've never been pulled over. Squeal tires, or have another car next to you accelerating at the same rate, or maybe even an overly loud exhaust, and now you've got problems.
If I see a car stationary at a junction, I can assume that 0.5 seconds from now, it will either still be stationary, be a little further forward or a little further back.
The range of possible positions is significantly reduced with an acceleration limit.
If some cars stop better than others, then if everyone slams the brakes on, the poor souls in cars that don't stop as well will collide.
Keeping a safe distance between cars mitigates this though.
I suspect you'd have a lot of the car industry against your campaign though...