I'm in no way saying it's the only, or even the best, way to set up DCs and scaling. I've GMed a lot of RM, which uses objective target numbers, and where PC bonuses really mean "mechanical progression" and not just "story progression". And if I was to start running a different game from 4e, it would probably be Burning Wheel, which uses objective target numbers as well, and in its GM guidelnes emphasises the use of objective target numbers to build immersion in the setting in the way that (I think) you have in mind.
The BW scaling was one of the things in the back of my mind when I asked the original question. For those that don't know, BW uses a dice pool system, where your "obstacle" (OB - AKA "difficulty") is usually in the 1 to 4 range for reasonable tasks, only going higher when opposed or doing very tough things. You skills and attributes can't go any higher than 10, which is 10 dice in the pool. You need one success per OB to succeed. Naturally, there is a whole host of other things that modify the OB and how the dice pool works, but that is the heart of the system.
This doesn't, by itself, create much room for scaling. But relevant to this topic, the BW equivalent of tiers is black, gray, and white dice. White is very rare, and would be reserved for superpowerful characters and/or very aged ones. Black is mundane, and Gray is the stuff in the middle--a dragon might have Gray armor and claws, for example. But characters don't move into a tier wholesale--they move from black to gray and gray to white with individual abilities.
There is, of course, a mathematical effect from changing to gray or white. Mainly, whereas a black die only succeeds on a 4-6 (on d6), the gray succeeds on 3+ and the white on 2+. You can calculate the odds of this, and except for being a bit confusing for those who aren't used to die pools, could be simulated with any number of mechanics. However, where it really shines in the sense of scaling is in the differences that happen by change in "tier".
For example, a character that manages the very difficult task of getting gray reflexes is incredibly fast in the "Fight" subsystem. More interesting, gray armor pretty much stops damage from black weapons. But the best aspect is that even a starting character that is very skilled has the option to trade a lot of dice for an upgrade in tier. There is a huge difference in play between a gray 3d6 and a black 8d6. The gray character is sacrificing current ability for future, greater mastery.
So if we assume for a moment that d20 + mod should limit the mods at around 10 (as several have suggested), and that DCs should be set accordingly, a corresponding system might be adding multiple d20s when "skill" gets high enough. This still preserves the possibilities of failure on normal DCs, but radically shifts the odds towards success. But mainly, like BW, if you name those shifts to 2d20, 3d20, etc., then you can attach meaningful new effects, that will change the nature of how the game feels.
I rather suspect that blind mathematical scaling without much in the way of overt changes to mechanics is what makes 4E feel a bit blah in this regard (and 3E a bit out of control). (I'm aware that 4E has extra powers at the tiers which change things, but we are talking strictly the feel of the mechanics here. I'm sure there is something equivalent in 3E, but those don't change the mechanics either.)