Personally, I prefer static DCs as framed by the original post, as it seems like everyone else does.
I do think though that scaling DCs are kind of an innevitable consequence of a high-variance resolution mechanic like a d20, and high power level scaling.
@djotaku makes the important observation that
Which is true. A professional rock climber will (almost) always succeed at climbing walls that an amateur like me will always fail at. In fact, a professional will probably always succeed at tasks that a hobbyist will always fail at, and the hobbyist will (almost) always succeed at tasks that an amateur will (almost) always fail at.
For a d20 system to accommodate this, a regular professional would need something like a +35 modifier to their roll. If the system wants to facilitate a zero-to-hero story arc, they need to scale their bonuses from around +5 to around +35 as they level up. That means an interesting challenge for a high-level character will be completely inacessible for a low-level character, and an interesting challenge for a low-level character will be trivial for a high-level character. So in order for the game to stay interesting, the DCs will need to scale with the PCs' levels. Hopefully, there's some in-universe justification for this, like low-level characters climbing fences, and high-level characters climbing smooth faced buildings. The low-level thief steals from peasants in the dark, and the high level thief steals from the King in broad daylight.
Some alternatives are narrowing the range of play, using different dice, and auto-succeed.
Some games narrow the range of play, having PCs start out as competant hobbyists, instead of amateurs with potential. This works pretty well as long as you don't care about the zero-to-hero arc. Depending on implementation, it also runs the risk of flattening out character diversity. If every character is at least competant at everything, there's less to differentiate my character from yours.
Other games just use different dice. With a d20, a +5 bonus turns your 50% chance of success to a 25% chance of success. With 3d6, that +5 turns 50% into a ~95% chance of success. Because of the bell curve, you reach "almost always succeed" a lot sooner, and flat DCs stay relevant a lot longer. Some groups like the unpredictability of the d20 though and like seeing exciting crazy results on a nat 1 or nat 20.
Finally, there's the auto-succeed. Some games, explicitly or implicitly, tell the GM to just not roll for easy tasks, regardless of what probability of failure the dice would give. There's always a subjective judgement call here, and in my opinion, it "feels" kind of inelegant, but it works for plenty of groups.
