Suppose you want a system where you want to signal to all internet companies that you don't want your browsing data to be harbored without your consent. The ID system would allow the creation and enforcement of such system.
The support for this comes in part because of pressure from the groups who are concerned about privacy and fretting over how their browsing data is used. While infringement of privacy hampers the growth of ecommerce, complete ban on harboring data hurts e-businesses (they won't be able to advertise efficiently). The solution to it is to create a free market: assign everyone a unique id, to which your preferences about harboring date will be assigned. Even better, data associated with that id can be considered proprietary, and users can license it to companies who are willing to pay for it and users can sue companies that infringe on this proprietary data bc courts will recognize it as solely yours. This is a good start if government wants to step in to protect your privacy from the "evil" corporations, while not hindering the growth of e-businesses.
Ideally, you will be protected from corporations who are after your private data. Government, however, will surely continue using it the way you don't want.