Well, yeah, humans are prolific breeders which makes them ideal hosts for the Yeerks. The Yeerks only need three to create thousands of babies. A man can have children from puberty to death. And a human woman can have as many as twenty children in her lifetime assuming she starts from puberty and has no complications along the way.
I think this a discussion that could get very graphic fast, so without trying to sound like I'm backseat moderating, lets just keep the mechanics out of it and stick with the most superficial details.
Well said, on both accounts.
Hork-Bajir weren't part of evolution, they were created by the Arn. As such it's unlikely that they have been around long enough as a species to become incredibly numerous. We also know that their life span is shorter than ours, and it's quite possible that the Arn purposely put a limitation on how fast they would breed, in order to prevent over population. There's also the virus that the Andalites used to decimate the Hork-Bajir population, so it would've taken a long time to recover their numbers.
Taxxons were implied to be numerous, and we can make an educated guess that they breed in a similar fashion to Earth insects (producing massive numbers of young to make sure a small number of them will survive). As well as any natural threats they may have originally faced before the Yeerks showed up, the fact that their entire race are cannibals would have severely limited their numbers.
Gedds are mostly a mystery, but we know that they weren't very intelligent and that their physical forms were far from ideal. This would most likely mean that they were vulnerable to predators, disease and death by other natural causes common to non-sentient (or barely sentient) beings.
The Yeerks may only have one Andalite host, but let's cover them anyway. Obviously due to their tail blades they no longer have to fear predators, and their advanced technology greatly decreases the number of natural deaths. However, they live in small groups spread out over huge areas, which essentially prevents mass breeding.
Andalites are very traditional in many ways, perhaps indicating that they don't allow children to be born outside marriage. We know that they are very ritualistic, and that as well as morning and evening rituals, they practice a wish-flower ritual in preparation for the birth of their children (possibly suggesting that children cannot be born/conceived until the ritual is complete?)
Admittedly some of that is speculation. However, Elfangor himself tells us at the start of Andalite Chronicles that the Electorate had recently voted to allow more children to be born. Due to the ongoing war with the Yeerks, they said that possibly 3 or 4 children might be allowed per family. This would seem to indicate that it was very rare (perhaps even illegal) to have more than one or two children.
In conclusion, it's pretty clear that in the Animorphs universe, a sentient species as numerous as Humans is highly unusual. We have a high birth rate and since we are highly adaptable, we have been able to spread across the planet so that we appear less crowded (It's implied in Andalite Chronicles that humanity's habit of adapting to a wide range of living environments is unique).