I believe that in a manner not unlike the "what the customer wanted" swing cartoons, the "PC progression math" of 4e started out with a rather simple objective that gradually got more and more complicated.
The first, rather simple idea: To make adjusting monsters on the fly easy for the DM, increasing a monster by one level should increase its attack bonus and AC and other defenses by 1, and its hp by a number (6 to 10) according to its role.
Step two: This creates a 29-point difference between a 1st-level monster and a 30th-level monster. In order for the PCs to keep up, they need to gain about +29 to attack rolls and AC and other defenses between 1st to 30th level.
Step three: Level-based increases should take care of some of the difference. We'll go with a rather simple 1 point per 2 levels, instead of a more complicated formula like 2 per 3 levels or 3 per 4 levels. That takes care of 15 points, leaving us with 14.
Step four: Ability score increases would further close the gap. 3e gave +1 to an ability score once every 4 levels. To make it easier for the players to remember, we'll give out a +1 to two ability scores at every level ending with "4" or "8", and at the start of the Paragon and Epic tiers. That makes +8 to two ability scores, which accounts for another 4 points, leaving 10.
Step five: Traditionally, we also have enhancement bonuses from magic items. Since they can now go up to +6, that leaves just 4 points. We'll have a variety of methods to close the final 4 points: some feats, some item bonuses, some powers, etc. Most players would have one or two of these, and even if they don't, a four-point gap probably shouldn't be crippling.
So you see, if they were willing to use more complicated formulae for monster math or PC level-based increases, we wouldn't "need" magic items to balance the math: a 2/3 progression (+20 over 30 levels) would reduce the "required" bonus from magic items from +6 to +1, and a 3/4 progression (+22 over 30 levels) would eliminate it entirely.