In an environment where everyone is equal under the law, large corporations would lose their special protections. They would no longer be protected by double standards. If they were sued successfully in a Rights Enforcement Agency's court or similar and chose to ignore the finding, they would lose the protection of that court in the future. There would be consequences basically for them ignoring such "private dispute resolutions." Their customers would be made aware of their decision too. Who would continue to do business with them then? Sure, it is not a perfect system, but a company's reputation would matter. Companies who abused their power would pay a price for that abuse within the market.