Good post
@Mercurius , with a lot of thought put into it.
Just a few notes and observations...
World Population of D&D Campaign Worlds
The world population in 1500 AD is estimated to have been about 450 million. That's the high Renaissance - which seems to be about the level of most D&D kitchen sink campaign worlds, or at least like the Renaissance, portions of D&D worlds have that level of technological and society development. But different campaign worlds would have different population levels. Looking at Earth again, we could consider different eras and their respective populations:
Early Industrial (1800 AD): 1 billion
Renaissance (1500 AD): 450 million
Early Middle Ages (1000 AD): 250 million
Late Antiquity (500 BC): 100 million
Early Antiquity (2500 BC): 20 million
Late Neolithic (5000 BC): 5 million
So the first thing one would have to do is decide which best suits their world's basic societal era. I would think that the Forgotten Realms would be closer to Early Industrial population level, considering the existence of multiple races, the Underdark, and greater population density than Earth (i.e. there are few vast areas with little population, unless vast regions of Earth during the Renaissance).
A points-of-light or low fantasy, Sword & Sorcery style world might have 20 million or less. It really depends upon the world.
The variable this ignores, however, is magic. Life expectancy is the biggest cause of population growth/shrinkage after resource availability, and magic could both extend it (via curative and support magics) and reduce it (by making it easier to kill lots of people at once). How a society approaches and-or regulates magic will make a big difference to that society's growth rate, and thus to that of the world as a whole.
This also means that by the time you get to Early Industrial you're diverging rapidly from the real world, as some if not all of that industry would be replaced with magic (particularly if the setting denies the existence or creation of gunpowder or similar, as many do).
Never mind direct life-extension magics which, though rare, can make a difference; as can progression into immortality and-or intelligent undeadness.
Prevalence of Leveled Characters
But even if taking the latter approach, we must remember that a level implies a degree of training. A farmer who serves in the militia during the occasional orc attack is not a fighter, but a warrior. Class = training. This doesn't mean that training has to be rare, but it is significant.
You're assuming that training has to come from someone else, right? But what about self-training?
The farmer in the militia who gets a taste for it and spends every evening practicing on her own with sword and bow is almost inevitably going to learn some things from doing so. The lone woodsman who eventually learns enough about woodscraft (probably through trial and painful error!) is going to slowly become a low-grade Ranger. And so on.
Spellcasting classes are different. I could see a Cleric self-training with guidance from its deity, or a spontaneous caster self-training with guidance from its patron or whatever; but book mages are probably out of luck - they'd need external training.
Given all that...
Very Common (1-in-10 or more): A lot of folks pick up levels, whether because the world is dangerous and training is common, or because it is just that kind of world. Or imagine it this way: if you interact with a dozen people in a day, one or two of them are leveled.
Common (1-in-100): Leveled characters are plentiful, with most villages have one or even a few, a handful in every town, dozens in small cities, hundreds in larger cities.
...my world would probably be somewhere between these two on average, though the actual numbers would vary widely depending on culture. For example it's quite possible that 3 Elves out of every 4 are levelled now or have been at some point during their lives, where it's also possible that of a community of 1000 Hobbits you'd be lucky to find one with any levels at all.
Distribution by Level/Tiers of Play
But a simple way to address this question would be to ask: For every one "legendary" character (level 17-20), how many paragons, heroes, and apprentice adventurers are there? Is it 1 to 10 to 100 to 1000? Or is it more like 1 to 100 to 10,000 to one million?
I would posit three ranges:
Soft (x10): 1 to 10 to 100 to 1000
Moderate (x50): 1 to 50 to 2500 to 125,000
Hard (x100): 1 to 100 to 10,000 to 1,000,000
One, albeit formulaic, approach is to imagine that the amount of leveled characters that ever make it to the next level is half. Meaning, of a 100 1st level characters, 50 make it to 2nd, 25 to 3rd, maybe a dozen to 4th, six to 5th, three to 6th, or two to 7th, and one or none to 8th or higher. If we extrapolate from one 20th level character for every level, and then add up the tier totals, we get the following:
For every 1 20th level character, there are 15 total level 17-20 characters, 1008 level 11-16 characters, 64512 level 5-10 characters, and 983040 level 1-4 characters. Or to put it another way, only about one in every 65,000 1st level characters make it to 20th level. That doesn't seem that far-fetched, if you think about it.
But you could also imagine a "softer" progression. Maybe a greater percentage make it to higher levels.
The one factor that really blows up all these sort of formulae (and I've yet to see or think of a mathematical workaround) is - of all things - PC adventuring parties and, if such exist, their NPC counterparts.
Why is this? Because a typical adventuring party, along with any associates, represents a number of people all rising together in level in a rather short time; and the presence of that "bubble" at any level throws off all the numbers. So if your played party of 5 PCs make it to 20th level you've now got 6/65000 rather than 1/65000; and this forces the question of how many other parties have done this in the setting's history and of those, how many members yet survive.
Further, and this would come down to individual DM preference in some ways, in order to challenge your 19th-level PCs and get 'em to 20th there always has to be a bigger fish; and not every DM wants to look off-world to find said fish. This means that there's likely to be a number of very high level people out there who are villains-in-waiting: mad wizards, liches, small-w warlords, etc., and these have to be factored in as well.
My incomplete thoughts on this lead me to conclude that the shape of the distribution isn't a nice neat triangle with low level at the bottom and high at the top, but more like a beaker: triangular-ish at the bottom but morphing into almost a narrow tapering tube or cylinder at the top, with a very high upper extreme.
Put another way, while at lower levels 1 of every 2 (or even 2 of every 3 at extremely low level) might drop off per level, at higher levels (in 5e, I'd guess 10th+) the dropoff rate might be more like 1 in 3 and by 15th you might only lose 1 in 10. Game mechanics would expect a significant dropoff between 20th and 21st, but from there it's open-ended (aside: I don't believe in hard level caps in any system) to aloow for levelled entities powerful enough to be a challenge for those 19th-level PCs.
