I collected the millennium issue like this:

In the middle is the souvenir sheet. On the top and bottom are the two stamps from each page in the book. They are gutter pairs (like yours.)
Of course, I also have the book itself in its pristine shape.
As to why would some one cut up the book? So that stamps that are awkward can be displayed in the collector's regular album.
For example, press sheets are almost impossible to display. But a collector can still display a piece (like the Titanic s/s missing the colour dots) or a gutter set of blocks from, say, the insect series to prove that he/she has a complete collection.
When upbraided for destroying a sheet, one can always pull out the original kept in storage.