From reading the responses, I'm thinking that it would be a mistake to fuse tiers to the core system and that they should, instead, be used in a modular fashion to define different approaches to campaign styles and character development. So I've got some ideas in that regard.
First of all, a DM (with the agreement of the group) can decide whether to start a "Classic" or "Heroic" campaign; in the former the characters would start at a power level closer to AD&D - not quite 1E, but somewhere between 1E and 3E. In Heroic, the characters would start as established (albeit minor) heroes, somewhere in the 3E to 4E range. The difference could include anything from starting ability scores to number of HP, feats, and something akin to what I was calling "Heroic Talents" which would be a modular option to bring back a bit of the 4E power feel. In the Heroic game, for example, a PC might get a Heroic Talent at 4th and 8th level, or something like that, that begins to set him or her apart from your everyday folk.
In this approach, further "tiers" become modular options off of the Heroic tier - Paragon at 11th, focused on Paragon Paths; Epic tier at 21st level, focused on Epic Destinies; and Immortal tier at 31st level, with Divine Traits and later, possibly, Spheres of Influence.
The key here is that each tier is a modular option; if one wants to simply play the Classic game, they go from 1st to 20th or 30th level without any of that "extra jazz"; power curve is flatter and more realistic to real-world developmental patterns. But for those wanting a more powerful, epic fantasy feel, the tiers are modular options that can be added on.
A further modular option would be similar to 1E's 0-level characters, an Apprentice level that could be played as a kind of prequel to the Classic game.
Now of course one potential problem with all of this is that it further complexifies what could potentially already be a confusing situation with tons of modular options. But if the design goal for 5E is to provide different play styles, in addition to a basic/advanced bifurcation being required to appeal to both those who want a simple rule set and those that want a more complex tactical game, I would suggest that WotC needs to do the same with what I'm calling Classic and Heroic campaign styles, and that--as opposed to my original post--these don't need to be fused to levels.
I would also add [MENTION=2804]Dragonblade[/MENTION]'s idea--which I was thinking about as well--that the tiers are akin to options that the game group can either choose or not choose to "open up," and even choose when they want to open them up. So you might have the Classic game as the core and the, starting at something like 5th level, the group can either choose to open up Heroic tier or stick with Classic; if they choose Heroic, they get a Heroic Talent and maybe an increase in ability scores. Then, starting at 11th level or so, they can choose to open up Paragon tier, at which point they choose a Paragon Path and another increase in ability scores, with further increases and Path-related powers through the next ten levels. Then, starting at 21st level they can choose to open up Epic tier and choose an Epic Destiny with further increases as with Paragon tier. The same with Immortal tier starting at 31st level.
The point is, that all of these tiers would be optional. Perhaps each would require the former; one couldn't start Epic without first having gone through Paragon and Heroic, but there is flexibility as to when these could be started, and they would be added onto the normal level development. A 25th level character in the Classic game would be a great warrior or wizard, but would still be "mundane", ability scores maxed out around 20, and no tier-specific talents, paths or destinies that accent their class and race-based powers. Or a 25th level character could be superheroic, with ability scores in the mid-to-high 20s, with special powers from the various tiers.
Again, exactly how this is done is not as important right now than that there is the possibility--but not the necessity--to open up higher powered tier equivalents.