In any game I've ever played, the world at large remains the same, regardless of whether you're level 1 or level 10. It's not like the level 10 party goes walking through the forest, and all of the goblins are suddenly replaced by ogres. High level characters are objectively much more epic than level 1 characters, but that comparison only means anything if the world itself remains objective.
If you're playing through a linear adventure, then it doesn't matter whether or not your stats improve much, because your opposition is tailored to provide a challenge. You'll never be very impressive, next to what's in front of you. In a sandbox game, though, you actually do have the opportunity to do amazing things - because you're as likely to encounter a low-level obstacle as a high-level one. A powerful sorcerer can take over an empire, because the NPCs don't automatically scale up to oppose them, so your massive bonus to Diplomacy checks can actually mean something. An epic fighter can reliably climb a smooth wall, because the wall doesn't suddenly develop a teflon coating when a high-level character approaches it.
Bounded Accuracy exists so that high-level characters can still be challenged by easy tasks, which is mutually exclusive with high-level characters stomping all over easy tasks by virtue of their epic power.
Pathfinder in sandbox mode is a lot like Exalted. The GM asks you to roll in order to do a thing, and you succeed by some unreasonably huge margin, because you're amazing.