AbdulAlhazred
Legend
If you look at the math of 5e's treasure allocation, it basically hands out 1 permanent magic item per 4 levels and 1 consumable every level.
It isn't necessary to hand out a permanent magic item every level - that leads to bloat by requiring a ridiculously large number of good magic items to create differentiation. If you can only have 3 items that work(ala 5e), everyone's a little bit more different than they are in 4e.
Sure, my scheme just says "well, an item, a 'feat', etc are all just 'progress'". So you could have no items at all, or one ever per PC, or one per level. Beyond that I envisage that there can be some variable amount of 'minor boons' that don't produce a level up. Those would just be story-based things that the DM can give out or players can acquire just as there have always been. Obviously the rate of reward of these things might have SOME impact on game balance, but basically my response is that nothing is perfect, and in any case the DM can always just say "yeah, FOR YOU that's a major boon, it might be trivial for the wizard, but for the barbarian the Badge of the Berserker is serious stuff!" You could simply decide that if a character was 'sandbagging' and picking up lots of minor boons while avoiding level ups that they just level up regardless. Because it's really a pretty loose criteria its easy to bend. The main goal is to keep characters of similar power being binned together in the same level, or at least close. This is really after all what level is meant to do, measure the actual power of the PCs, just like for monsters. By flipping the logic of "level up to get more powerful" on its head to "get more powerful and you level up" MANY issues suddenly go away.
Obviously progress could still drive a superabundance of items, if the game designer(s) and/or GM simply neglect other alternative boons, but my feeling is that there would be a natural tendency for things to drive forward. Nor does it seem like it will be terribly difficult for the GM to come up with reasons to grant boons for narrative reasons. "Yeah, you sink your sword into the heart of the Red Dragon, his blood covers you, and you taste its metallic tang on your tongue, power seems to surge through your body!" etc etc etc. All stuff you CAN do in 4e now, but the game is just presented in a way that is somewhat fixated on items and has this somewhat artificial distinction between things you acquire by narrative and things you acquire by mechanics.