Absolutely, but various kinds of transactions involve third parties. Imagine a company that provides a very specific service and contracts its accounting or other secondary functions to a third party. Should we prevent the principal company from dealing with a third party in such cases? Not necessarily.
I think a partial solution is to be very clear about third parties and to give consumers a genuine option to prevent disclosure where third-party intervention is not needed to provide a service. Prohibiting a company from doing business with a third party would obviously protect privacy, but do we need to go that far? I don't think it's necessary.