For some kinds of information, like medical records, the information is deadly not to have accurate, but also deadly to have accurate and public. Once the information leaks, employers might decide to not hire high-risk people or insurers might decide to pass over certain people as too costly.
I'm of the opinion "anonymizing" data is something that enables grifting; if enables the collectors to placate the people they are pulling data from, and it allows the grifters to make the argument the information they have means nothing.
Ultimately, I think these organizations should be making sure their information is absolutely accurate, and we should have laws in place, with severe criminal penalties, against the use transfer or use of said information. I would even go so far as to say things like cell phone location records should be fully public as a matter of the law.
Now when you want to get those records, you go to a government website for the "hunt and poke" stuff (e.g. where are my kids going or is my wife spending time with another lover, how long is my commute on average, or where was I at 3 years ago on a day, all sorts of useful questions); the access records are public too.
If you want to study them, you sign a NDA saying you won't, under penalty of severe criminal prosecution, leak the information or use it for criminal purposes. Anyone found having the data and no signed government NDA = instant 20 year prison sentance plus felony conviction.
This way, if, for example, someone signs the NDA and goes on to offer services to executives to help them cherry pick staff, not only does the person offering the under the table services go to jail, but the executive does as well.
When you criminalize certain things, then give the public all the information and tools to do as they see fit, the law works. It's a lot easier to prosecute a company executive for cherry-picking staff with insurance data when the data is well-labeled. It is also a lot easier to sue them when you have an access record that says someone under their employ checked how often you go to a clinic or night club via your cellphone records.
The problem is not going away anyway, and "anonymizing" data to placate our sense of morality isn't going to help. There is no easy technical solution, but if the thinking is not to anonymize but instead track and enforce who has access, things change drastically.
That aside, I would like the option that says "do not collect the data". It wouldn't even be hard.
Sure there is knowledge and advantages in that data, but that doesn't even come close to the benefits of privacy. Think the general public opinion about X is pretty stupid? If so, you'll need it too.