One of the explanations for the seemingly omnipresent giants and dragons myths is that they come from the discovery of dinosaur fossils and mommoth bones. I'm wondering if there's also a possible explanation for the "little people living in the woods", especially seeing as completely disconnected cultures seem to have independently relayed this myth.
Although prehistoric animal bones are often put forward as an explanation for dragon beliefs, there is not proof of this, nor is it accurate to suggest that there are dramatic similarities shared by Asian and European dragons. These are popular misconceptions that serious scholars discount.
The same can be said of exotic explanations of the various "little people" who appear in various cultures internationally. While you are correct to point out that they are likely disconnected - by descent from any historical common ancestral tradition - I would first point out that they are also not necessarily that similar. That said, what similarities that do exist are best explained by the shared aspects of the human experience.
For analogy, let's consider the international beliefs in ghosts. In this case, there may be an argument to be made for descent from a common ancestral belief system, given the fact that belief in survivors of death is ubiquitous. But common/shared or not, what are the limits of these traditions? A universal aspect of these traditions is the necessity to explain why we don't see the dead even though believers maintain that they are frequently in our midst. Ghost traditions can be separated into two general forms: the walking corpses and the spiritual remnant. The latter solve this problem by usually being invisible. Sometimes we glimpse them, and those anomalies become that "reports" that support and sustain belief. With walking corpses, the solution is to relegate the phenomenon largely to the dark, when we cannot see things clearly.
Similarly, belief in nature spirits is ubiquitous - and there may be a path to consider, again, the possibility that there is an ancient inheritance from a shared ancestral belief system, but here things are much murkier than with ghosts. And yet, believers in supernatural beings of nature face much the same problem that is encountered with ghost traditions: if nature spirits are ubiquitous in nature, why don't we see them all the time? The answer must be that they are capable of invisibility or that they are very small - or both. And like ghosts, they are most often seen at night when they are more comfortable to travel about - because it is harder to see things when it is dark.
Here, it is important to point out that the solutions are not universally applied. The complex of fairy, sidh, elves, hidden folk, etc. of Northern Europe arrived at different solutions for the problem of entities being ubiquitous and yet hard to see. Many - the Irish, the Cornish, and the Danish people - regarded the entities are spending most of their time (but not all) in small form. In Sweden, Norway, and much of the rest of Britain, the entities spent more of their time in human size - but here, the potential for invisibility was underscored. Hence the names from Norway to Iceland that emphasizes the "hidden" aspect of the hidden folk. In all cases, the ability to become invisible existed, but in a few places, small stature was an added explanation for the reason why we rarely see the entities.
The point here is that diverse unrelated people may have a similar beliefs - spirits living in nature; but then they were/are faced with limited ways to explain their ubiquity. Many people were/are consequently drawn to an explanation that these entities are small, and that is why we usually do not see them. The similar aspects of these diverse traditions do not require a profound theory of explanation. It's simply a reflection of the limits of the human experience.
We see a very different solution to the widespread traditional belief in giants: while many people have traditions about extraordinarily large human-like entities, these is the repeated problem of explaining why we haven't encountered them since they should be easy to see. In this case, a common solution is to relegate them to a distant time or place: "There used to be giants, but they lived long ago," or "there are giants, but they live far away [in Wales or Cornwall for the English; or in Finland or eastern Russia - depending on where the bearer of tradition lives]."
The point, here, is that diverse unrelated traditions often arrive at the same notions, answering similar questions with similar solutions because there are limits to what the world around us offers by way of explanations. This does not mean that there is some deep hidden cause for similarities. Why are most (but not all) supernatural beings bipedal with two arms? Because it is easier to imagine these entities to be like us than otherwise. Of course not all are, but the common human experience affects the way most tradition manifests.
I am a little surprised to see that no one has mentioned the aspect of these little people as frequently living underground, such as the Native American belief that a race of small people reside inside of Mount Shasta; also the Sidhe of Ireland and the elves of Iceland. This would fall under the heading of explanations for why they are not (more) often encountered.