So now that I did all that work, I find that I don't like the results.
It assumes that an encounter with a total XP that could generate a CR opponent of a higher tier must necessarily be a one-mob encounter. The instant you make it two mobs, the XP per mob drops back down to the current advancement tier. When considering several enemies, there's also the XP multiplier that boosts each mob's effective XP.
For example, suppose we have a level 4 party, on their last big fight before going to level 5. Let's also say we're always going to keep these big fights at 'hard' level, not 'deadly', as the DMG numbers seem mostly tuned for hard fights to be the loot hoard generators.
XP per player is at least 375, but less than 500, for total party XP of 1500 to 2000. To get a CR5 fight, you can use 1800 XP on a single mob.
If there's multiple mobs, you base the loot table on the highest CR creature. With 2 mobs, you could have a CR4+CR1, or a CR3+CR2. Or progressively larger groups with smaller CR numbers. But fundamentally, you cannot have a CR5 with more than one mob. That also implies that getting tier 2 loot while the party is tier 1 is quite low. Single-mob fights tend to be very do-or-die. If you can counter the primary threat, they're fairly easy to take down. If you can't, you die.
So, let's revise tier 1 to not get any tier 2 loot.
Next, tier 2.
Level 8: 5600-8400 XP
Level 9: 6400-9600 XP
Level 10: 7600-11200 XP
CR9: 5000 XP
CR10: 5900 XP
CR11: 7200 XP
CR12: 8400 XP
Again, a single mob fits within the XP range, but...
2 mobs:
CR9: 7500 XP
CR10: 8850 XP
CR11: 10800 XP
CR12: 12600 XP
3-6 mobs:
CR9: 10000 XP
CR10: 11800 XP
CR11: 14400 XP
CR12: 16800 XP
Two mobs with a CR11 lead would fit at level 10 (though even then, the second mob would cap at CR1), but three or more mobs prevents anything higher than CR9 from being used as a lead.
So it's
possible that you might have one tier 3 encounter while at tier 2, but it's pretty unlikely to get more than that.
Next, tier 3.
Level 14: 15200-22800 XP
Level 15: 17200-25600 XP
Level 16: 19200-28800 XP
1 mob:
CR15: 13000 XP
CR16: 15000 XP
CR17: 18000 XP
2 mobs:
CR15: 19500 XP
CR16: 22500 XP
CR17: 27000 XP
3-6 mobs:
CR15: 26000 XP
CR16: 30000 XP
CR17: 36000 XP
You can't have 3+ mobs with CR17 lead. You can barely fit in 2 mobs with a CR17 lead, but the second mob would be near-worthless at this level. You could do 1 mob with CR17-18.
Once again, I will allow that you might have one above-tier treasure hoard at level 16, but that's about it.
So, revised graphs:
And one comparing 5E with the estimated Pathfinder wealth levels, as provided by CapnZapp:
And this is the spreadsheet number distribution:
This seems much more workable in terms of having an appropriate amount of wealth at any given level within a tier, though the last level may get you a running start towards the next tier.