I think the reason is pages do not exist as primary objects in Writer. They are allocated on demand when a page is full (this includes the case of shifting lines as a consequence of widow/orphan management).
Page overflow is discovered when it happens but what is already laid out, remains as is.
I discourage you from any attempt to vertically justify your page: pages are consequences of text flow. Any edit prior to the page in scrutiny may change the location of the page break and all your tuning will be ruined.
Also there are two ways to justify pages: play with paragraph spacings (but this may leave white space at top and bottom) or with line spacing. The latter way implies to modify the paragraph styles, creating styles unique to a page and you end up with zillions single-use styles which is not the way of using Writer. In this case, better go for full direct formatting, causing, in this exceptional case, less difficulty than styles, but you lose style flexibility. Also, line spacing applies to a full paragraph; so, unless your paragraph start and end are synchronised with page breaks (how? this is not implemented in Writer because, once again, pages are consequences not causes), your fine-tuned line spacing for one page will badly interact with the previous and next ones.
Last but not least, any attempt will conflict with your desire to have a single content source for three editions (see your 258664/in-book-publishing-how-best-to-change-the-page-size-for-a-new-edition question.
What you request can be done in DTP (e.g. Scribus in FOSS or Quark XPress in proprietary software) but it becomes tiresome when the book has more than 10 pages.
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