Nothing except for large segments of the population that will revolt at the very idea. Politicians win by promising to be "tough on crime" regardless of the real result. People like to think most others are much, much worse humans; and they like to see them punished for it to reinforce their belief. Paying a drug addict to get clean won't be popular, but paying people for driving "normally" won't fare much better.
I agree, though, we would ideally keep some/most existing laws and fines while cutting back on the number of officer-hours to make the immediate costs balance.
Since positive reinforcement is generally more effective than punishment, we could apply this idea across society.
Why pay police officers to sit on the side of the road all day, pulling over speeders and writing citations? How about automated cameras that can randomly reward drivers with $10-$20 for driving the speed limit? Shouldn't we expect more safe drivers and less overall expense?
Even if it were proven effective, the reason it won't take off with traffic or medication is that most people want to see wrong-doers punished more than they want to see less wrong-doing. Don't take your meds? You deserve your illness. Speeding (even though I do it too)? You deserve your $250 fine. You did the right thing? Woopty-do. What, you want a cookie?