It starts off with the people emigrating to other earths. The authors make a point of how people step at a rate of 10-15 minutes per earth, yet we meet settling parties in places that would take decades of constant stepping to get to. Clearly, no one thought to work out travel times when stepping, even as they were writing a book about traveling through stepping.
I don't think that's a constant. You can be a natural stepper, or just a "good" stepper, in that you don't get sick from it, and step around once every couple seconds, though you'd still have to stop enough times to find food, rest from carrying supplies, or make camp for the night. Larger groups seem to step at a rate of 10-15 minutes per Earth because the average person gets queasy from it, and the more people you have, the more often you'll run into problems stepping too quickly. And there's also the people who can step through the "soft places"... they can get to millions of Earths away in a single step if they find the right place. I think there's enough variation there in how fast stepping can be done to explain the people and colonies that are found so far out in the Long Earth.
But not getting exponential growth? I mean, just not having heard of the concept? I don't know how long it would take Trolls and Elves to fill up the long earth, but it wouldn't be long. A hundred and twenty thousand years after the first Troll/Elf is born, all the earths are deserts, at a guess.
Homo sapiens before behavioral modernity and before agriculture didn't actually grow their populations so fast. Elves, Kobolds, and Trolls are all hunter-gatherers with few examples of behavioral modernity on the level of
homo sapiens, so to me it makes sense their population growth would be very slow, even if resources and space is abundant on the Long Earth.
The stepper town would have been hit with every plague in history, untill they developed a psychotic hatred of strangers. Aslo, Romans on an empty earth with 2000 years to work, and they got a couple of little towns?
Happy Landings seemed to be getting around 25 new arrivals a year from the Datum, so that would only be 50,000 arrivals from 1 CE to 2000 CE. They would be growing that population through natural growth, of course, but it seems the population of that world would still be minimal. Not all humans would want to stay around, I'm sure, especially because the society tolerated Troll inhabitants early on. I'd bet much of the Pacific Northwest was colonized, with settlements elsewhere in at least North America, if not further.