I would be more interested in the period of when Moria was thriving - when they wrote the password for the back door right above it. Meaning, those must have been one of the most peaceful periods in the wider regions history. How dense was the population at that time?
Sauron had already returned c1000 TA to Dol Guldur. We're specifically told that evil things, such as Orcs, begin multiplying in number by c1300 TA, which triggers the migration of the Hobbits to the Shire (already we have an example of why there's less people than we expect.) In c1400 the Nazgul begin their long destruction of the disunited (perennially entangled in civil war) kingdoms of Arnor. In c1500, Gondor is embroiled in devastating wars with Harad. In the 1600s a Great Plague depopulates the North and West: "many parts of Eriador become desolate"; not long before, Gondor has had a horrible civil war. During the plague, even the Shire suffers "great loss." In the 1800s Gondor is again involved in a costly war, this time against the Wainriders, and loses its eastern territories. In 1981 TA Moria falls. In the 2400s Gondor is again under a major attack by (though they do not know it) Sauron, and Sauron is able to use the Orcs in the Misty Mountains to effectively cut off Eriador from the rest of the continent. in the 2500s, the Gondorians are bailed out of a major disaster by the appearance of the Rohirrim, but shortly after, the dragons appear and decimate the dwarves. In the 2700s, after centuries of Orc attacks in the region, the Hobbits themselves defeat a band of Orcs; shortly after, Dale and the Iron Mountain fall to Smaug, Rhoah is nearly destroyed, and Gondor is attacked by fleets of Corsairs. In addition, there is a devastating winter that causes "great suffering and loss of life"; in the same century, Smaug annihilates Erebor and Dale, and there's a major, costly war between the dwarves and the Orcs.
In the following centuries, there are continual major Orc attacks. In 2900 Men finally abandon Ithilien. In 2911 there is another devastating winter, and the year after, great floods that result in the desertion of Tharbad and Minhiriath.
The Hobbit begins in 2941. Orcs have been in force for 1600 years.
The black death is a better real-life comparison point, and Europe actually took a lot of time to recover.
One of the more common last names in Norway is still "Ødegaard", literally "Deserted farm", reflecting families who were residing on farms which still had not gotten a proper name by the time the tradition of using your fathers first-name as a last time started dying out. This even then - by the 1800's - involved re-clearing farms that had still not been re-settled after the Black Death.
Of the ca. 36500 farms which existed in Norway around year 1300, only about 16000 were still populated by 1520, and the population is believed by some sources to still have been only half of what it was in 1300. It was not until the 17th century that Norway "recovered" - that is, until it was back to pre-plague, levels, having lost several centuries of growth, but with population centres having changed, leaving many ancient farms still empty reminders.
In Norway, a disproportionate portion of the political and religious elite died. E.g. while almost the bishops in Sweden survived, all but the bishop of Oslo died in Norway. The Northern provinces of Norway were left to their own devices for a long time, without a functioning government, because so few government officials were left that the king chose to focus restoration in the South and largely just abandoned them.
That was one event.
I also don't recall running into Nazgul and Orcs while growing up near Oslo, and imagine facing that might have been a rather severe deterrent to growth.
EDIT: I'll add that Norway is a good reminder that a combination of destructive events, harsh conditions and the extremity of the hockey stick nature of population growth can explain a lot. Norway today has a population density of ~14 per km^2. In 1950 that would've been ~8. In the mid 18th century about ~3. In the aftermath of the plague, likely <1, and still <1 by the 16th century. You can still travel on foot for days through central Norway without meeting people if you stay clear of the places most popular with people out hiking for fun. A couple of centuries back, and not only would you be able to do that, but you'd have been likely to now and again come across farms that had been empty for centuries, despite centuries of a growth and recovery.
But you did have trolls, right? :)
It’s 1600 years of an active, organizing intelligence whittling the West away and which saw the _destruction_ of multiple major kingdoms and settlements prior to the beginning of the story. The people of Arnor were nearly exterminated as a result of the Witch-King, for example. These were not wars like medieval wars. They were wars that entailed abject slavery or genocide for the losers.
not well defined, but it was time of significant progress in metallurgy and magic, for example greater rings of power were forged at that time.
The Great Plague some time before and the Long Winter are explicitly said to have depopulated Eriador and left it "desolate." The Rangers were also not infallible. Obviously they did nothing to stop the Nazgul or large numbers of Saruman's agents in the time of the Lord of the Rings, nor did they stop the Orc-band that invaded the Shire a hundred years before the story.
If the population density was low to start with, and food production tough, recovery from even a single major enough event can take a very long time.
> From what I've found, most of Europe recovered population size before 1500.
Hence the reason I pointed out that Norway did not, to show that the range of possible outcomes is substantial.
Differences for Norway included a harsher climate, and a landscape that in most of the country is not conducive to large scale farming in a constrained area (outside of a tiny part of the South East, even the "flat" parts are not particularly flat, and often rocky terrain), combined with a very low population density by European standards to start with. As a result, in a lot of places, while people had productive farms, the farm locations depends heavily on the terrain and are often spaced out, and a lot of focus was on e.g. raising sheep (which could, and still are, be let out to roam the mountain sides during the summer months). Recovery faced a lot of challenges, not least of which was simply that in parts of the country the next farm over might be many hours walk over tough terrain away, and during months of the year trying to go to the nearest village might be hazardous (winter months), or people might be up in the mountains far from people. There are still a few people living in places not reachable by road in Norway (and not just by the coast where they could compensate with access by boat). There are still large parts of the country where if it wasn't for cars getting from village to village might many places take days of walking (often horses or carts would not have been an option due to terrain).
Families could go the whole year without meeting any outsiders, and as a consequence marrying off your children and ensuring the family line survived, was a major ordeal in many parts of the country even when you had plenty of food, because the production of that food in Norway, even when the climate has been "good", has meant the farming part of the population has been spread out far more than many places.
There were no major cities. By the 1600's, Bergen, now Norways 2nd largest city, with 285k people, was by one source described as "definitely the largest city in the Nordics" with ca. 15000 people, as a result of being a major Hanseatic league trading port, but while it was larger than e.g. Copenhagen, Denmark (and Sweden) had many other cities of some note, Norway did not. The old capital, Trondheim, by then had reached 5000, and the other current cities in Norway had far fewer.
Even today there are parts of the country which if you avoided car travel would seem almost as desolate as in LOTR, and the population density today is more than 10x higher than before the Black Death. In the 150 years following the Black Death, you'd have walked through a landscape that would have appeared mostly untouched by man, with the very occasional farm, sometimes days apart, which half the time would be in ruins, and the very occasional small village.
Yes humans can repopulate. And thus their era arrives. Thus your objection isn't a plot hole but part of what makes Tolkens work so interesting.
It’s not really possible to attack the orcs in their mountain homes for anyone except Dwarves. And even Dwarves understood their limits. In the War of the Dwarves and Orcs (TA 2793-2799) they sacked every orc stronghold from “Gundabad to the Gladden” but even then did not dare to enter Moria, where orcs remained secure and continued to multiply.