Actually, just the opposite. I'm quite a fan of WotC's level tier system, and think it worked very well... the only reason I made changes to it were strictly economic decisions.
Then I don't understand why your (initial) proposal ends at level 20?
The biggest two complaints I saw of of the Red Box were that 1) it was not really replayable and it expected you to immediately buy all the Essentials material immediately after. And 2) the rules of the Red Box game did not actually feed into the game as a whole, so that if/when you bought the full Essentials game, the character you designed via the Red Box could not actually be used and had to be rebuilt.
I basically ignored that part because it doesn't make much sense to me in a discussion about tiers. Both complaints can (and should) be addressed in different ways:
1) is difficult to solve, considering the restrictions of a low-cost entry-level product. I don't see any satisfying way to increase replayability without increasing cost, and fiddling with (existing) tiers won't help at all (see below, though!).
2) would have been easy to avoid - I have no idea how WotC botched this! It wouldn't have been difficult at all to ensure the characters stayed compatible with Essentials. The only excuse I can think of (and it's not a good one) is a rushed release. But where's the connection to making changes to tiers? I don't see it.
So to fix these two issues I figured the following: whatever the so-called Starter Set boxed set included... it had to have enough levels in it to make it a standalone game that a new player could replay several times if they wanted (just like players of the Red Box in the BECMI days could). 5 levels seemed to make sense for that.
Well, the BECMI Red Box covered only three levels, so five levels is probably too much. Considering a trend I'm seeing in this thread and one of the often-mentioned criticisms of 4e what I could see is something else:
4e doesn't have a 'mundane tier', everyone starts out being a hero at level 1. To address that a box would have to support game play at, say, levels -3 to 1!
Then you could indeed start as a (talented) nobody: Instead of starting the game with two at-wills, 1-2 encounter powers, a utility, and a daily power, you'd gain them step by step in levels -3 to 0, ending up with a regular level 1 heroic pc.
That would also offer more (re)playability without increasing the required box content by much.
Now the other tier-based boxed sets can easily cover ten levels each, with a minimum of overlap in the heroic tier for level 1.
As an additional incentive, I could imagine getting a small benefit for playing through levels -3 to 1 instead of simply starting at level 1. E.g. it's plausible you'd start with a magic item, gain an extra feat or trained skill, etc.