I don't know the precise legal mechanisms for handling diffuse harms like the ones you describe. Determining the best means of applying the principle of suing corporations in practice is an very complex question that belongs to the philosophy of law. My task here is only to establish the nature of the principle and to show that it is practicable.

That said, here is my principle: at any time, the government is orders of magnitude more powerful than any corporation. I think it is proper, in some cases, for the government itself to act as a plaintiff, to aggregate evidence, bring suit, and prove causation statistically. I can't delimit that role precisely, but I side with you that in some cases only the government has access to all necessary evidence.

And no, I don't agree with the idea of "public interest." Any claim that "the public interest" supersedes private rights means that the interests of some men are to be sacrificed to the interests of others.