The bit you’ve missed is that the cabin altitude will not rise to 8000ft if you’re cruising low. Most aircraft try to pressurise the cabin close to the max allowed pressure differential (delta p) to keep the cabin altitude as low as possible. If a 777 starts cruising at say FL320, you may find the initial cabin altitude is about 7000ft. I’m plucking the numbers out of thin air (no pun intended) but hopefully that gives you some idea.