Some rules are in a world because they sounded dark, and my free Fantasy World Keystone has three tests that cut five candidate truths to the three that carry weight: https://thetaletinkerer.com/the-keystone?v=TtRCFSKZn7g&p=pinned

It’s also possible to have the maiden altar as described in a larger settlement. From your own numbers, the maiden altar won’t work in a settlement of two thousand, but in a settlement of six to eight thousand, it’s possible. And as others have observed, you also assume the sacrifices provide no tangible benefits. For videos about fantasy, you work very hard at not permitting fantasy elements to affect societies.

The solution was those that were going to be killed anyway.
Short explanation: instead of just executing the bandits captured, they fed them one a year to the lich that for reasons his own, protects the town.
This was the setting I dropped on my D&D players.  A lich that's protected by the town because the lich protected the town from other kingdoms and larger problems like young dragons.  The only thing he wants is a yearly soul and he wasn't picky about it.

One thing to consider: cities don't grow by births alone. In fact, historically, more people were dying in cities than they were born. Cities mainly grow by attracting people from countryside. Because of that, thay can have much faster growth than their current size suggest. They can depopulate much faster too, if the economic opportunities that were drawing people in suddenly cease.

Funny how similar the described mechanism is to how army recruiting worked in the Russian Empire when the military service was 25 years long. There were lists, there were rotations, there were squabbles, bribes... because the person being sent as a recruit was basically dying for his village. And the communications from the Gods of Bureaucracy were all too real - if the village didn't provide enough recruits ("enough" was decided by the same bureaucracy), they communicated by punishing the village up to sending some troops to capture some men...

One sacrifice every lunar month?? I've never heard of anyone who sacrificed at that rate. Once a year would be more realistic or even just infrequent occasions like lunar eclipses or major conjunctions

You forgot to account for the fact in fantasy the sacrifice can have tangible benefits that outweigh the cost.

The economics of human sacrifice. You might have animal sacrifices on most years and save the humans for special circumstances, like a famine when it's harder to feed everyone anyway. That way you can have the threat without all the bean counting.

Basically, There's actual math behind why most adventures with cults have you saving a Sacrifice who wasn't a part of said cult.

6:29 I remember reading that in the short story unit of my 9th grade English class. I was the first person in my class to recognize what was going to happen, because I was already familiar with the setup because a book series I’d already read invoked a similar image. As soon as they started drawing the lots, I knew it was going to end in death. I was one of the only people in my class who wasn’t shocked by the ending.

There's actually a solution that makes this even darker, for those inclined to edgelordery

The town sacrifices maidens to the gods, and to make up for the lost mothers, its men take war brides from neighboring civilizations.

If you really want grimdark bullshit, there's usually a way to make it work.

London was a population sink - not because of human sacrifice, because of disease. But the inflow from rural areas seeking jobs not only kept the population up but increased it. So your world needs something to attract people to the Temple town.

I'm curious where you got the idea that fantasy (games or literature) sacrifices one maiden every full moon? First, most places wouldn't do human sacrifice at all. Animal sacrifice, perhaps. Second, major holidays aren't once a month, major holidays are once a year or four times a year, usually at the equinox or solstice. Also, since human sacrifice is an evil act, it would be mainly evil societies that did such, and they would have no problem kidnapping or raiding their enemies for potential sacrifices. Why cripple their own society for it?

It would make no sense for a cult to only take its victims from one town, especially if it tries to keep its activities secret. The roads are rife with travelers ready to be plucked, and those arteries connect to other nearby settlements. The Thuggee cult killed millions on the Indian subcontinent, with one cult member (Thug Behram) being involved in 931 murders and personally strangling 125 victims. During their peak activity, colonial records estimate that bands of Thugs killed upward of 30,000 to 40,000 travelers every year.

Plus, if you make the mistake of selecting the hero's love interest as the sacrifice, you've just invited her boyfriend and his merry band of do-gooders to show up and disrupt the ritual, quite possibly at the most breath-takingly inconvenient moment...

Now here is the important bit: you sacrifice those who can't or won't contribute - most often children and rivals.

You forgot something in your calculations about the Aztecs.  Aztecs sacrificed relatively few females, perhaps one to every 6 males sacrificed.  A city can't sacrifice daughters without population crash, but the same doesn't apply to sons.  This is, after all, happen with some frequency when populations lose most of their males to war.  It doesn't take too many males to fertilize all the females, but if the female breeding capital is damaged, the population numbers
suffer seriously.  That is why Aztecs sacrificed warriors captured in battle with far more enthusiasm than "bathed slaves", the best class of female sacrifice.

Did a different way. A wise and beloved ruler was revered and venerated by his people like a demigod. The court mages enchanted a magic pillar, which drained 1 day of life from each individual who touched it, and bestowed it to the king. The tribute was voluntary; he asked the kids to be exempt, but old and sick people touched it repeatedly, some to the point they died. A population of 5 million people. 5 million days. The king thus became a demigod, having his lifespan increased by more than 13 000 years. This way the sacrifice didn't become a "population sink".

In a real world context, it's more likely that human sacrifice might be something of a last resort in desperate situations rather than a regular monthly event.

The Carthaginians are reputed to have sacrificed both their noble children and captured enemies to Moloch. Recent archaeology suggests that many of the "sacrificed" children were actually natural infant mortality re-branded as dedications to the god with genuine sacrifice only being documented (by their Roman enemies) when Romans were actually at the gates, primarily when Regulus was there during the First Punic War. The Romans, too, practiced human sacrifice, although it's often glossed over; the most notable case was a single Vestal Virgin entombed alive after the defeat of Cannae during the Second Punic War.

Current archeology for Tenochtitlan is putting forth the theory that the Aztecs may have had less than 200 sacrifices across the entire span of that empire's history. It would seem most likely that their rate of this was on par with that of Europe's public executions in that same era, or less. What they did have was a lot of blood letting in ritual self cutting. To the point of things like using obsidian shards on their own tongues, and other methods, as a way to pray or show devotion. And they had propaganda. Both their own and that of their enemies. They wanted to be seen as fierce, so they put out a reputation of it, and their enemies (long before the Spanish arrived), propagated that very message as an argument to fight against them. When the Spanish arrived, they had no reason to want to dispute this, though it is curious how it all just 'suddenly stopped' the day after Tenochtitlan fell to the Nauhuas / Mayan allied invasion... and only a generation later Aztecs were serving in the military of New Spain as it 'nothing had ever been going on' to make people hate them...

There's a lot of this kind of thing in history - where we have records of a massacre or a tradition of brutal war leading to glory, and then archeologists show up and prove none of it ever happened. From 'Biblical' to Roman to Aztec, there's a pattern of that.