No the problem is that you again scale the DCs like 4E advises you to do. A river or a cliff does not automatically become a trivial challenge to 9th level PCs because they don't get better at climbing/swimming automatically. And just because you are hunting a lvl 20 BBEG you can still encounter such obstacles.
It is just not true. Climbing a slippery vertical masonry wall is a DC 26 check. This makes it a level 10 hard DC, thus such a wall would be appropriate for a level 10 character. Given the hit points of level 10 characters the height of the wall might easily be in the 10 squares range (IE around a 50' wall, most characters would require at least 2 rounds to climb this, assuming they don't do anything else, 4 rounds if they move carefully, 2 or even 1 with Spider Climb depending on if you use both actions). Falling is likely to result in a loss of at least 10 and as many as 40 hit points. OTOH climbing a dry brick building facade with cornices and sills is about a DC18, a hard check for level 1. You'd likely only climb 2-3 squares at level 1. These DCs will NOT change if the PCs are higher level. A level 10 party encountering the level 1 wall will find it fairly easy. A wizard with +6 Athletics at that level would still need a 12 to make that climb however, far from automatic, he'd be well advised to employ some magic if the consequences of failure are a concern. OTOH if the level 1 Brutal Scoundrel with the 14 STR, training in Athletics and a background bonus (+9) happened to decide to climb the baron's keep (the level 10 climb) he could at least attempt it, though it would be VERY risky (he'd need a 17 to succeed and a 12 to avoid falling outright). However, if he was clever enough to bring a rope and a grappling hook he could increase his odds substantially. MOST of the time you wouldn't have this sort of challenge laid in front of level 1 PCs, but its not completely unheard of, players try strange things. Likewise there could be times when higher level players will try easy things like level 1 climbs.
You can run a 4E game like 3E, but there is no point in it. As everyone is good in everything in 4E all challenges must be scaled to their level or they are trivial. A 9th level party comes across a door? If it is a normal door everyone in the party can overcome it. To be really worthy of actually being a challenge it has to be a adamantium door with a clockwork lock. In the end you still just have a scene with a generic obstacle. It doesn't even matter much what the obstacle is as everyone gets better at everything. The level of the PCs decide what door they face.
The whole point is the narrative, so of course it matters. Not only that but again check the DCs for things, a 9th level wizard will NOT find a locked door of even the most trivial sort easy to open, he'll in fact require a fairly good roll to open it. He COULD however at least TRY, and why not? Clearly if you wanted it to be really hard you'd have made it a reinforced door. That would signal "worthy challenge" anyway.
The thing is, you make it sound like the DM is somehow always obliged to turn all doors to adamantium at Epic. It really doesn't work that way, its just that Epic PCs do not worry about mundane doors, its beneath their level of concern.
In 3E this is different. Here the exact nature of the obstacle matter much more as PCs are not automatically good at everything. The best lvl 15 lockpicker in the world will still have trouble scaling a moderately challenging cliff if he never bothered to train climbing. And when they face a door it is just a door appropriate for its location. Maybe the rogue int the group is good enough to open it, maybe not.
Sure, so you lack a way to determine what is genre appropriate for level 15 PCs, that's the problem.
And the broad skills in 4E reinforce this "skills being redundant". You are good with athletics? Congratulations, you are a good swimmer (despite never having seen water deeper than your knee), climber (despite the highest elevation in your home country just being a mild 300 meters), etc.
That's why it is called Athletics, its "I am Athletic, I do these things", not "I've specifically practiced every one of these sports". 4e doesn't really provide a specific way to call out "I'm BAD at this one thing", but the opposite problem is true of 3e's system (and DDN's) where you can't call out a whole broad range of things you're good at. At least in 4e not every strong guy HAS to be a good athlete, whereas in DDN that's the only option since STR check are all going to be good for that character. Nor do I have a problem with talented characters being good at something right away. RPGs are never perfect at modeling these things, but I've met any number of people who did something really well the first time just from sheer talent.
Someone being good in Athletics, Perception and Streetwise tells you nothing about that person as every category is so broad. It works for "hero" characters who are awesome at everything (Climbing, swimming, running, spotting, listening, gossiping, etc.). And that is just three skills. Considering that under the 4E system you get good in everything it means every PC is a walking superhero. But some people still want their characters to be humans with flaws and weak points. Those weak points are denied in 4E as it could result in someone not participating in an skill obstacle scene and that obviously wouldn't work with skill challenges.
Again though, you are just wrong. Nobody is "good at everything", they are CAPABLE of anything, but that's FAR from the same thing as good at it. 4e DOES insure that every PC's talents are moderately broad, but the guy with Athletics, Perception, and Streetwise is not going to be especially good at knowledge tasks, nor social tasks. He's going to be pretty good in the 'exploration pillar', and at least has a good option in a more socially dominated 'town' type setting. Depending on his ability scores he's probably got anywhere from one to four other skills he's moderately good at (IE untrained but has at least a +3 bonus, maybe even as high as +8 in a few cases). The point is, yes, adventurers are well-rounded, but this is not exactly new, in OD&D and AD&D 1e they could do anything except a few very specific things that were covered by class features.
In 5E it seems to be the same, just less drastic. Because of the flat math everyone has a chance to do nearly anything and the space where a trained person can succeed and a untrained person can't is very narrow (because of the huge variance the D20 gives).
The problem in DDN is that you don't really advance in much of anything significantly. If a 10th level ranger and a 1st level fighter have an archery contest who's likely to win? Its not clear at all that it will be the 10th level ranger. There's very little difference in the 2 characters to-hit with a bow, and it doesn't change much as you go up in levels. Sure, the level 10 ranger will be SOMEWHAT better, but 5 or even 8 points between a character who is supposed to be a renowned expert and one who's merely competent seems pretty narrow. Clearly things like 'skill dice' are supposed to fix that, but I don't see the point of these extra complications. I have a couple other issues with DDN skills, but that's a big one right there.