The thing is, there's more than just a difference of scale if you can find out a bit of data about one specific person, or a handful of specific people, and if you can find out that bit of data about the majority of the people in a population. There's a difference between being able to find out specifically if Jo Doe is a member of group X, and being able to find out all the members of group X and noticing that Jo Doe is in that group.
People can be targetted - for advertising, for harassment, for enhanced surveillance - if public information is available in the aggregate, in ways that they cannot be targetted if the information is not.
There are some types of data about individuals, where it is in the public interest for that data to be available, but it also represents an invasion of privacy if it is. So the public benefits have to be weighed against the potential for harm. The thing is, the potential for harm changes depending on "how available" the data is. If the decision on whether to make data public was made in a time where getting individual pieces of data was time-consuming and inconvenient, and getting data in the aggregate was near-impossible, then if the data suddenly becomes available in the aggregate to anyone with a passing interest in obtaining it, the trade-off that was made to determine whether the data should have been made public is no longer valid.
So saying that something is "public information" is... tricky. There are cases where we should look back at the trade-offs we made, and re-evaluate them in the light of the technology that is now available to the average person.