Alternately, there is an implicit suggestion that challenges in high-level locations will involve things other than Cave Slime.
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Fixed DCs encourage graduation to new types of threats instead of just variations on the same old threat: Ultra Slippery Acidic Cave Slime.
I think this is a big problem in the HPE modules published by WotC for 4e - they manifest exactly the problem of repetition that you state here, and therefore don't display the meaningful progression of the fiction that the core rulebooks (in the tier descriptions I quoted upthread) talk about.
Instead of worrying about slipping on cave slime you worry about a qualitatively different threat, like whether the dragon whose cave you're slipping into has emplaced Symbols of Insanity in the chokepoints. Or rigged an Explosive Runes to blow up the dam and drown you.
To me, qualitative threat progression (tactical ==> operational ==> strategic) is way more interesting than just scaling up the quantitative DC ("it's really, really slippery slime") of a familiar threat.
4e doesn't really emphasise the tactical to operational to strategic - or rather, the fiction can change in this sort of way but mechanically much of it will still be skill challenges (but the fictional framing of the skill checks takes on a bigger scope).
But 4e does do a good job of the first sort of escalation you describe (eg Symbols of Insanity in chokepoints). On the player side, you see this sort of thing in powers that open up new conditions (eg stun, dominate) and new forms of movement (fly, decent distance teleport). So the tactical context, both for exploration and for combat, changes quite a bit as the PCs gain levels.
Just amping up the Cave Slime won't play to these features of the system - as the HPE modules tend to demonstrate.
I'm going to call on [MENTION=6696971]Manbearcat[/MENTION] at this point, to see if he has any views on how what I've said fits into his reply to you on this point upthread.
4e produced a sort of super heroes like kind of aesthetic where high level characters really aren't much troubled by the ordinary muck and dreck of existence. The interesting thing is, in that system you can simulate the effects of luck, fate, an evil plot, whatever, by simply placing a level 20 cave slime in the path of a high level character who's 'walking down the street'. Its a sort of natural thing to do in fact. What is the fictional justification? Luck, fate, evil plot, run with it!
I think the use of levels (and associated mechanica elements like DCs, etc) to represent luck, fate, etc is an interesting aspect of 4e that certainly moves away from "objective" DCs.
You see this in other mechanics, too, like the Alexandrian's favourite "besieged foe" or the bonus to damage a marking target that a heroslayer hydra gets. What do these represent? They give the game a narrative dynamic or a "fate", wherein certain heroes find themselves beset at the centre of the fray.
Personally, this is an element of 4e that I really value - I find it helps give the game a mythic, epic feel in play. My extensive experience with Rolemaster makes me believe that it is something much harder to achieve in an "objective DC" game where every die roll is expected to be correlated in some fashion with a causally understood gameworld process. You can try to introduce gameworld processes to model luck, of course, but as soon as you give them the sort of mechanical and rule-governed tractability that fits within an objective DC framework you've already lost that sense of whimsy or myth (as the mood takes one) that I think 4e is able to convey.
Fifth Edition doesn't have rules taking into account that you're trying to tell a story
I think this is contentious. (Hence whether 5e is a good vehicle to evoke the sense of a world infused by luck, fate, myth etc that I just described is probably also contentious.)
Have a look at [MENTION=5834]Celtavian[/MENTION]'s post 1034, and [MENTION=6787650]Hemlock[/MENTION]'s post 1038. And also the Inspiration mechanics (which are pure player side - NPCs don't earn Inspiration - and affect PCs' chances of success).
That's not to say that you mightn't ignore all those features of the system if you wanted to. But then you could run 4e with objective DCs if you wanted to, by drawing on the doors and environmental hazards tables and extrapolating a bit from there. (Much as 5e is going to require some extrapolation, too, to assign "objective" DCs to every gameworld element.)
And somewhat as a side-effect, to prevent narrative dead-ends, it chooses to define the world in such a way that Bounded Accuracy is the result.
Not following your second comment here. Care to elaborate?
Obviously I'm not Saelorn (and not a Saelorn sock-puppet either!), but here's my take:
A consequence of Bounded Accuracy is that, even if you set DCs based purely on a sense of "objective" features of the ingame situation, you're not going to accidentally dead-end your game (and hence bring the narrative to a sudden halt). This is because even the highest DCs are feasible relative to the spread of bonuses, because of the Bounded Accuracy feature of design.
I think that [MENTION=2067]Kamikaze Midget[/MENTION] was making a similar point (or maybe at least gesturing towards it) when he talked upthread about the inclusion of a dragon or a balrog in a low-level adventure. The DC spread ensures that this isn't just a dead-ending for the PCs and hence the narrative flow of the game.
Having stated (what I take to be) the point, I think it's a bit of an open question whether it's completely correct. At least at the extremes, you can have PCs who can't make DC 25 or 30 checks (eg dump stat, no proficiency). And in the combat case, the damage that a dragon or balrog can pump out might make the fact that low level PCs can meet the DCs to hit it pretty irrelevant.
