Isn't that what organizations like the ACLU are for? Except ACLU fights for civil rights whereas your hypothetical organization fights for consumer rights. The reason why it doesn't exist is that it suffers heavily from the free rider problem. Any individual's donation of $20 or whatever is unlikely to get them $20 worth of returns, because the lawsuit is either funded or not. Moreover you'd benefit regardless of whether you donated or not, so there's no incentive to donate.

But isn’t that true of the ACLU as well?