Saddle-stitched booklets have a stitch (usually a metal staple) holding the pages together which also forces the book covers apart into a "fan".
The covers require a spine.
Add an extra bit of material between them to compensate for the thickness of the booklet. It will more nearly resemble a case-bound book. Score the cover at the appropriate space, 1/8," 3/16," or so for up to 8 pages.
This works so well because the two 90° folds on either side of the spine will lie flatter than the one 180° fold stuffed with the pages holding them apart.
Attach the "signature" to the inside-back cover very close to the spine with double-sided tape or a bead of cement. You tip-in your booklet "signature."
Then, trim the booklet for a finished look.
Off topic: This also causes a problem referred to as page "creep" where the gutter margin in book signatures must vary to allow for the thickness of folded pages. The centre pages stick out more than the outside pages. This must be taken into account when designing thicker bound documents. It is called "Page Imposition" software or stage of publication.