Businesses are much faster at inventing ways to abuse people than governments are to regulate them away, even if we ignore lobbying and corruption.
Such a hypothetical organization we seek needs to be both swift and impactful. This automatically suggests some ties to government, as it's the best way to fulfill the criterion of impact. Not sure how to handle the "swift" part, though. Can't do it through regular market mechanisms, because ultimately price trumps all on mass market. The government reacts slowly for (among others) a good reason - while an unscrupulous businessman needs to invent just one weird trick, the government regulates away whole classes of tricks by default, and they need to take care to not outlaw perfectly legit new ideas.
"independent" is doing a lot of work here. Government regulators are, at least in theory, independent because they're paid from taxes collected, and have no incentive . What mechanism is supposed to keep the new 'independent' entity, actually independent?
How it's designed is important, but even under the most elaborate schemes it would be less costly and human resource intensive than having the government directly take charge of it.
The formation of something new, and independent, means it would also be less susceptible to corruption.
Given that this is one of the primary purposes of governments, what do you suppose has been keeping them from stepping in so far?