There's a bit of talking past each other going on here.
What 4e does well is it answers the question: what DC should this be if I want my characters to have, say, a 40% chance of success, or a 60% chance of success?. That is, it's relative to the party. That's why it scales - higher level party, higher DC's, to have the same chance of success. The DC might mean different things depending on the DM and the context (a 40% chance at level 1 might be a well-made lock, a 40% chance at level 30 might be the gates of the lock on some trapped god's cage)
One of the criticisms of that is the "treadmill" - higher level characters face higher DC's and so have the same chance of success regardless of level - the item changes, but it's only superficial.
That's certainly a good starting point. I think I might have some more to say about that further on.
5e's answer to that criticism is that it answers a slightly different question: how hard is this task for someone to do? That is, it's relative to the world. That's why it doesn't scale - the lock on an imprisoned god's cage isn't a lower DC because the party happens to get there at 5th level rather than at 30th. The level of the party doesn't matter, it's still a DC 25 (or whatever) task. Thus, a party that manages to get to the cage at level 3 is going to have a more difficult time unlocking it than the party that gets to the cage at level 20. It doesn't give you the chance of success at a particular level ("never tell me the odds!"), because it doesn't want to keep a tight lid on the different bonuses and options a character might bring to bear.
My only disagreement is the idea that there's a notion that in 4e you'd change the DC if a level 5 party stumbled into your level 30 adventure. I don't think 4e's rules are intended to answer that question, and thus this use case is not envisaged. Now, maybe if such an eventuality came up, that's what you WOULD do, but I don't think we can know without a lot more context. I would think in general that if you were introducing level 30 content into your level 5 game you'd plan that ahead somehow.
The big change is that the DM in 5e shouldn't worry much about what the party is capable of, they should worry about how difficult this thing is in the world. You can chuck a DC25 god-cage-lock at your 1st-level party. It's up to them to figure it out, or come back later, or pump up one person's ability check, or bypass by slipping the halfling in between the bars...
I don't think this is really different in ANY edition. In fact in a sense this kind of thing is ALWAYS in play. For a given party it is generally an environmental assumption that walls are impenetrable, that you can't really defy gravity, etc. Any variances on these sorts of assumptions are explicit, or involve very high level PCs. Likewise the unpickability of the lock of a mad god of secrets by level 1 PCs can simply be considered a given. You wouldn't really need to assign a 'DC' as such if this element was introduced into the level 1 play. Logically its a thing the PCs might have to establish by trying to pick it, as there are level 1 pickable locks, but presumably even in 4e the players would simply adapt and come up with a solution when picking didn't work.
I guess my point is that I don't see it being more or less possible to introduce 'differently leveled' content into one system or another. Every system has a way to say "you can't do this, do something else" inherently.
That's one of the ways that 5e encourages organic gameplay moments. Where 4e would tell you, "give your players a 60% chance to succeed on most checks, vary it by a little bit occasionally, and the game will keep ticking forward," 5e says "put it on the players, and let them explore their options - they may surprise you, or not, but it'll be up to them to figure it out, not you to hand it to them."
So, from my standpoint the hard and fast aspect of this falls based on my previous observation. You can of course talk about the sorts of games that are ENCOURAGED by different rules presentations and content.
Above I said I might have more to say... I think what it is that while I don't know that the 4e devs really were committed to 4e as a 'story game' universally, it really in essence IS. In this kind of game you are always considering the implications of things, and working from the standpoint of what the dramatic meaning of a thing is. How does it figure into the conflict that is ongoing in the story? When you think about things that way, then you really wouldn't be concerned with the thought of a 'treadmill' of checks, or of 'objective world reality' either. You would be thinking about how to focus the story on the dramatic conflict that the players have directed their characters at.
So, when I think about DCs I think about what do the characters need to do in order to make something happen. What do they have to risk? What do they stand to gain? How could this impact the evolution of the character?
An example of the difference here could be secret doors. In my sort of dramatic action play of 4e secret doors can exist for only a few reasons:
1. Atmosphere - The door simply exists because it makes the scene cooler. Instead of the wizard's lab having a regular door, it has a secret door! There is no DC for this door, the PCs just find it. Its not an obstacle, just set-dressing.
2. Plot Logic - The door exists to explain some aspect of the plot. Perhaps the Princess's bedroom has a secret door because there has to be a way to explain how the Vampire gets in when the fighter is guarding the hallway. This door might thus be found ajar when it is discovered that the princess is missing. It could be possible to find earlier, possibly setting different paths for the adventure to go down later, or maybe the DM is being a bit more railroady and sets the DC to 'impossibly high', it will only be revealed as a fait accompli.
3. To delay or challenge the PCs. Maybe the characters will become trapped in this area and need an escape, can they find the door before the Gelatinous Cube reaches the end of the hallway? Stay tuned!
Note that in cases one and two there isn't any need for a DC at all. In fact this is often the case. It may even be that a really clever GM could devise multiple possible adventures that have the same location but only differ in terms of which elements appear to characters of what level. This might be more generally how a sandbox could work in a modern game, only certain parts of the sandbox appear to you at level 1. Later you might return to the same environment and find a whole different experience.
Anyway, my point is that I don't see DCs as a way of explaining the world. They aren't a descriptive tool, they are a proscriptive tool. They do describe the world, but their use is really to help frame things. A really better example might be a secret door that only appears when the blood of an innocent is poured on it. Will the character accept the moral implications of a heinous act? Or will the door remain unrevealed? (obviously there would have to be plot elements in place to frame this conflict for the PC). While DCs are useful, I try not to get too hung up on them, and when I use them extensively its to challenge the players by the totality of all the things they're attempting, not to just sling endless series of 60% success rate checks at them.
