We do have other approaches. That I can obtain your employment contract, take your picture as you walk in and out of buildings and when you visit the beach, figure out your birth day and who you hang out with...
...doesn't mean I'm allowed to or freely share/sell every detail of your life.
We could for example create a license or permit for gathering a type of data. Like: If you are a dating agency you can ask for peoples sex. If you are a head hunter you may gather data on employment history. If you have a taxi service you can ask for peoples address.
We could also adopt a government issued key for things like signing petitions.
Where the data is stored could also be subject to regulation. Its possible to keep access logs with specific justification for each bit of sensitive information accessed.