Take for the example Norway’s rules (cited below) that tax returns can be viewed by anyone, and the list of who viewed each record is also public. This requires limitations on how the data can be reproduced.

If you need to drive to see a clerk it’s a lot harder to get access, and that’s a reasonable barrier. The clerk can also have reasonable limits on how many you can request and whether you can make a copy. Each of these rules do have an impact on how widely information is used or disseminated, and can limit data mining style use. Note that some of these limitations (like preventing a copy) can be more difficult when accessing from a website.

So yes, there are many useful limitations than can be placed on sharing of data that have a real practical impact on privacy.