I think Page still gets a writing credit, it’s just the order of the credits that’s different.
No, Page is not credited at all with writing “All Your Love” or “South Bound Suarez” (since you made me pull out my In Through the Out Door liner notes, I found another). For both those songs, the liner notes say “Jones, Plant”. I always found it kind of interesting that Plant gats no writing credits on their first album, yet is the only one who gets a credit on every song of their last album (axcluding Coda)
Of course, if you do count Coda, you can add “We’re Gonna Groove” (Ben E. King & James Bethea), “I Can’t Quit You Baby” (Willie Dixon), and “Bonzo’s Montreaux” (Bonham) to the list of songs Page has no writing credit for.