Maybe this is a weird completionist/collector thing, but I dislike looking through the gear collections and seeing so many missing lower-tier pieces of gear. I'd personally like it if, when you get an item of a lower tier, it prioritizes those you don't have yet. There seems to already be some amount of priority in place when you don't have at least full blue (and to limited extent purple), but after that the priority seems to be gone. My guess is that once you have a higher-tier item, it considers the lower-tier pieces to just be "duplicates" for ilvl purposes.
I'm not sure how chests do their percentages, if it's all one pool (all characters&slots white-tier has X% chance, green has slightly lower Y%, so on) or if it's a tiered equation (1. determine white/green/blue/purple first, 2. from within that pool randomly select character&slot). It would be easier if it's the latter, because then a step could be added between the two that determines if any gear pieces from that tier are still missing, and if any are then that becomes the pool to draw from, and if not then it is drawn from the pool of all characters&slots.
For example: For ease of numbers, say you have 100 characters; that means 600 potential gear pieces for each tier. Let's say all of your characters have at least full blue tier, but you're missing 100 white tier items and 50 greens. When you open, say, an Electrum Chest, it will roll first with the chance percentages for tier white/green/blue. If it's determined you're getting a white-tier item, instead of drawing randomly from all 600 potential white-tier items, it would check and see you were missing 100, and it would draw from those 100; if it determined green, it would draw from the 50 missing greens; if blue, since you're not missing any, it would draw from the full 600 for your duplicate item.