I like your general principles, but halving per level feels like too aggressive a function here; it doesn't really emulate the baseline D&D world.
-snip math-
Our tier populations get distributed among levels however we like. Some ambiguity helps us as DMs
I understand what you're doing there. And ambiguity, indeed, is helpful as a DM. But a strict adherence to "tiered" levels and/or play is definitely not my thing.
Considering that PCs are unlikely to encounter
every classed NPC (regardless of their level) in a given population center, and I just make up these lists as a guideline for my own purposes -maybe spark a few potential plot hooks or beneficial connections for the players, reminders for when/if the PCs return or I need to lend some internal consistency to the world-, I'll stick to my simple "divide by 2" method to get things down on paper quickly without lots of <shudder>
math.
If I need an "uber wizard" or "unbeatable warlord" to appear, wander into, or be ruling a given place, that is exponentially higher level than the Classed Population equation "allows" or a competing party of inept-but delusionally self-assured- low level adventurers the numbers don't account for, I can just put them there.
Having a world full of 10th or 12th+ leveled NPCs (let alone 20+!?) running around, controlling everything and/or to be found pretty much anywhere, is really not my play style or my homebrewed campaign setting's norm. The PCs, assuming they achieve such heights of experience as, well, above 12th level or so, would be hero-champions among men, well known far and wide with songs and sagas told of their exploits. They would become members of an elite cadre of legendary figures in the world's [known/remembered] history.
So, achieving "Tier 4 or Epic" level classed NPCs isn't really something I am concerned about.