Except for searching rooms, where the chart is used to set the DC's for examples... why is this different from everything else again?
Also this doesn't in any way address the discrepancies in dynamic DC's vs. static DC's... what's interesting is that people are arguing totally different justifications for the chart and static DC's totally dependent upon personal interpretation.
So I guess at level 20 all rooms the PCs enter, be it an inn, a warehouse at the local docks or the BBEGs fortress are riddled with secret compartments, magical darkness and bleed into the elemental chaos and shadowfell at the same time just so that the high search DC can be justified?
You're both putting the cart before the horse.
The DM, not the PC's set the "level" of the challenge. Every challenge (be it a skill check, skill challenge, monster encounter, or whatever) has a level. For most relevant encounters, the level of the encounter is equal to the level of the PCs (give or take two). Encounters with levels much higher than the PCs level are typically too hard, those much lower aren't worth the hassle.
Most DM's set the level of the encounter equal to the PCs because that's the sweet spot of challenges. Monster encounters with a level near the PC's level are typically good fights, treasure of their level is typically good treasure, and DCs of their level are a good range of target numbers. This doesn't have to be the case though; just as if High-level PCs go into the woods to pick a fight with kobolds (encounter levels 1-3). PCs who use their skills on mundane tasks (searching an inn) will find the challenge non-existant and the reward unfulfilling.
So the inn might be a level 1 area. Why? Not because level 1 PCs stay there, but because that's the level the DM set for it. It WOULD be a good challenge for level 1 PCs. The warehouse might be level 5; the DM peppers it with level 5 monsters, level 5 treasure parcels, and level 5 traps. And level 5 DCs. Why 5?
Well, either he sets it arbitrarily (sandbox) or based on the fact that he knows his 5th level PCs are going there (tailored). The BBEG might be level 8, the stronghold of the drow level 11, etc. You get the idea.
So a level 1 PC doesn't need a 15 to climb a ladder and 10th level PC need a 25 to climb the same ladder.
The PC isn't setting the DC. However, a ladder in a "level 1" zone is DC 15, while a ladder in a level 10 zone is 25, probably because its higher to climb, made of human bones, etc. If the level 1 ladder ended up shipped to the level 10 zone, it wouldn't become DC 25, mostly likely it would be ignored; its no longer a meaningful challenge to climb the 15 ladder unless there is a drastic chance of failure (since everyone can take 10 and they have at least a +5 from level).
Of course, the game DOES assume your 10th level PCs are wandering around 10th level zones more often than they are 1st level zones. Near-paragon PCs usually have more important things to do than clear out kobold warrens. However, if your PCs turn left and end up in the Caves of Chaos instead of the Tomb of Horrors, you're going to be using that "level 1-3" line on the DCs chart, not the "level 10-12" line.
Are we all clear on this now?