Add an option for Pages shelf to act like a filter, i.e. suppress or hide elements on the sheet that do not relate to currently selected page. This will enable multi-page printing of sheets while properly reflecting the hierarchy.
If you understand this problem after reading the short version, there is no need to read further. Long version that follows just elaborates on the issue and explains details.
I will use the sample Coffee Chain data to explain. By design, and for good reason, if Market dimension is placed on the Pages shelf, and State on rows, then the sheet will show all states, not just those that belong to the page (Market) selected.
The idea being that page shelf is used to compare pages with each other, and the movement from page to page can also be animated - so it would be bad if at every page change the sheet layout gets re-shuffled, and it would be hard to detect changes and see the effect of animation.
On the other hand, Tableau has a clever feature where a sheet with something on the Pages shelf, when printed, will produce multi-page document with each element of the Pages shelf getting its own page.
However, if I wanted to build a report where each Market gets its own page on which only states that belong to that market are shown, Tableau can't do it. The closest thing that is possible is to use Market on Filters shelf and get users to repeatedly apply filter and print. It work OK for this example, with only four values in Market, but doesn't work well for dimension with 20+ elements.
When I am asked "There must be something that Tableau can't do but "Big BI" can, what is it?" I mention two main things - email alerts and multi-page reports with hierarchies.
Also, there are many posts on this forum where people come across this phenomenon (displaying all elements in each page, not just relevant ones) and it is clear that they don't expect this behaviour.
So here is my idea: add some kind of option (tick box or something) to the page shelf that will hide irrelevant rows/columns. The same option can also disable animation controls, as a hint that the animation is a bad idea in this case, and maybe show some visual sign that the page shelf is in that special mode.
Of course it is also possible to introduce a completely new functionality that makes multi-page hierarchical printing possible and will have nothing to do with page shelf. Whatever is easier...