The logic for that is that the suit is supposed to recover damages for actual losses (including whatever is necessary to cover pain and suffering, etc.), but punitive damages are supposed to punish and deter further wrongdoing. There's no logical reason why they belong to the plaintiff. You could still accomplish the punishment and deterrence by having the award paid to the government, but attorneys would not be able to claim 1/3rd to 40% of those awards as part of their fee in contingency cases.
Take away the financial incentive for lawyers to bankrupt companies with big punitive damage awards, and you'll solve a lot of the problem.
And yes, I'm a lawyer.