While 4th Edition explicitly spelled out tiers and the levels at which you crossed the threshold, as well as the assumed style of play, none of it was really enforced: though the denizens might change and the locations become more fantastic, you could be crawling around in dungeons in some form for all 30 levels.
In other words, you might stave off an invasion in the mid-Paragon, but you could just as easily do that in mid-Heroic or even Epic. The only constant that I observed is that each tier's entry level provided a power spike above and beyond what you normally get, namely a feat or power.
In the second-longest 3rd Edition campaign I played in we made it almost to 13th-level before having to call it quits, and in terms of scope nothing we did seemed intrinsically tied to our level. At 1st-level we were hired to find a magical axe in an undead-haunted swamp, and at 12th-level we had to find a (maybe the) medusa's head, which was part of a white dragon's treasure hoard.
The first time I ran Age of Worms the party got all the way up to The Spire of Long Shadows (level 14), which basically saw them exploring an ancient city to learn the origins of Kyuss. Up until that point they had explored an ancient cairn, then an underground temple, then a lizardfolk den, then a mind flayer's lair, participated in an arena to shake things up, and then went back to the original ancient cairn to explore more of it.
In both cases, it was more of the same, but the monsters were bigger and the spellcasters had more spells with increasingly game-breaking results.
For D&D Next, Mearls proposes a 20-level spread where you spend the first three levels as an apprentice, which culminates into what we have come to expect from a 1st-level character, the next dozen or so adventuring as usual, with the final handful devoted to realm-management and determining what kind of mark you leave on the world, similar to 4th Edition's epic destiny.
Ultimately I do not see the point of tiers. 3rd Edition did not have them at all, and in 4th Edition you were free to ignore them because they were not tied to any assumed scope or rules. For example, I imagine that you will be able to become king of a nation in Next prior to 16th-level, as well as rally armies to help defend said nation. I guess I am curious how this will be enforced/encouraged, and think that they should just give us the rules to use if and when we see fit.
Now, I do like the idea of making a "tutorial" level, or level even level range. It could be great for teaching new or younger players, or for players that want to explore their character's origin in greater depth (though I also like the bit about random story tables). I think a better approach would to take a page from Dungeon Crawl Classics and allow characters to start out at 0-level, or have characters that pick up enough "apprentice" levels transition into a standard level 1 "adventurer".
Maybe they could add in an optional module with a more granular level system, where whenever you gain a chunk of XP you get to pick a new level-based benefit (more hit points, skill boost, feat, class feature, etc), and transition to the next level once you purchase each benefit once.