Two questions here: did they survive (occasionally they did) and why didn't they usually thrive (the degree of survival generally can't be called thriving).

Peter Narvaez, The Good People: New Fairylore Essays (1991) includes an essay dealing with traditional Northern European elf beliefs in Newfoundland. I conducted research on the survival of the Cornish knockers in the American West: Ronald M. James, “Knockers, Knackers, and Ghosts: Immigrant Folklore in the Western Mines,” Western Folklore Quarterly 51:2 (April 1992), and there was a recent account by Bill Haglund in Nevada Journal, Nevada, Iowa - August 29, 2013 about the survival of troll beliefs in central Iowa.

These are only a few examples of survivals. The trolls in central Iowa can actually be regarding as thriving to a certain degree. I believe we can attribute this to concentrated clusters of immigrant population. The knockers - which became the Western Tommyknocker - is an interesting example of a European elf belief not only crossing the Atlantic and thriving but also diffusing among non-Cornish population. I collected a sighting of a Tommyknocker that occurred as late as 1952 in Golconda, Nevada from a Portuguese-American. The tradition survived in part because the Cornish were so well respected as miners that other adopted their technology, their vocabulary (Lode is a mining word from Cornwall, for example), and apparently their beliefs about the underground, eerie environment of the mine. The Newfoundland example can also be regarded as thriving, probably also because of a concentrated immigrant cluster.

Elf beliefs did not generally thrive, however. This is probably due to a number of factors. Immigrants often went to urban settings, and even in Europe, when rural believers migrated to cities, they often lost their beliefs. Immigrants often diffused among other groups so that they lost an ethnic critical mass in a community, and that weakened beliefs. Where beliefs survived within the mind of an immigrant, they were not likely to be passed on to a new generation, since children will echo the belief system of their peers more than their parents (the same is general true of dialect). Because North Americans did not have deep roots and they generally regarded themselves as being part of the technological, industrial cutting edge, beliefs in traditional, pre-industrial beliefs had little room to thrive.

And finally, beliefs tend to be tied to places: the elves have always lived within that mound over there - that sort of thing. So when immigrants encountered a new environment, it was difficult to conceive of the supernatural beings as having lived in a certain spot since the new arrivals did not have anyone to tell them that this was the case. It's a complex answer to a difficult question, but these were certainly factors in why European supernatural beings did not generally thrive in the New World.

The examples you cite of supernatural beings that thrive, to a certain degree, among North Americans are often based on Native American beliefs. Here we have a situation where the people who did live in North America were able to communicate to the new arrivals that "something lives over there" or in that lake. These stories did not often make the transition and become an active belief system among the new arrivals. They often were adopted for local tourism and were regarded as "quaint" stories. Sometimes, the new arrivals adopted them completely - the bigfoot tradition is a good example.

Everyone has folklore and most if not all people have an active tradition involving supernatural beliefs (ghosts and angels are active today in North America, and we can include extraterrestrials in the spectrum of possible beliefs). So it was predictable that once immigrants "settled in" in their new home that they would have a belief system that included supernatural beings. The only question was regarding what they would believe in. So we have an assortment of supernatural beings in North America: for the most part, European elves (and the various creatures under that broad umbrella) failed to thrive; the widespread traditions involving ghosts and angels thrived; and some indigenous Native American beliefs diffused to the new population and thrived to a certain degree. We can even argue that the elves survived and thrived in a way: extraterrestrials are "little green men" who fly about in the night sky, abduct people, leave circles on the land, and do many other things that the traditional elf did in pre-industrial Europe.

I hope that helps.

edit to make clear that "lode" is an English-based word rather than a word with Celtic roots, drawing on the language was widespread in Cornwall. Thanks to /r/CasualCasuist for pointing out my careless language in this regard.

For one thing, elves, trolls and dwarves (it's a pretty fluid distinction between all three) are often tied to specific places, unlike vampires or werewolves. In Danish folklore, for instance, giants/trolls are often tied to particular hills or mounds, especially the burial mounds that are a pretty common feature of the landscape here. Elves in particular were domestic creatures that would terrorize or help the inhabitants of the farms in wich they (the elves) lived, although a relatively common saying in Denmark is 'nissen flytter med', meaning 'the elf moves with you' (IE you take your problems and bad habits with you when you move). As essentially genius loci, the people who believed in elves would not expect them in America, and if there wasn't a corresponding Native American tradition, it would not translate well into an American context, unlike some of the creatures that you mention.

A book called Daimonic Reality makes the argument that the same mental phenomena that led people to believe in fairies is now seen as alien abductions/UFOs in America. Bright lights and orbs that fly around is usually how people described fairies, and if you compare people's descriptions of seeing fairies with more modern versions of alien abductions there's a lot of over lay in the details. So, they did survive, but changed context due to cultural differences. I always found that an interesting viewpoint.

My Nicaraguan's friend's mother saw a leprechaun in San Francisco. We pressed her about it, her English is excellent, and "leprechaun" was her choice of words. Needless to say, we found this very puzzling.

James Mooney, the widely-published Irish-American ethnographer active in the late 19th century and early 20th century, studied the folklore and oral history of numerous tribes, notably the Kiowa and Cherokee. It's felt that his Irish cultural upbringing made him more receptive to the tribal cultures. Prior to writing about American Indians, Mooney published two papers on Irish folklore for the Bureau of Ethnology in 1889. His widowed mother who raised him was "steeped in the folklore of Ireland" (Mooney 3).

I agree with /u/itsallfolklore and /u/LieBaron, that elves are European and tied to place; however, almost every mainland Native American tribe has a history with Little People, that more closely approximate pixies or fairies, in that they are about two-feet tall or so; tend to live in wild, rocky places; tend towards being extremely mischievous (taking and hiding objects); help out lost children; and love to sing and dance. Humans that encounter Little People universally spend far more time with them than they think. When they returned to other humans, they believe they've been gone for a brief period of time, when they actually have been missing for hours or days.

Mooney describes Cherokee Little People here. While Cherokee Little People have been written about extensively, I've heard of Hopi, Comanche, Anishinaabe, and many other tribes interacting with Little People.

I suspect it's because fairies are highly localized — associated with specific areas. For instance, in both Ireland and, more recently, Iceland roads have been moved because of elves'/fairies' traditional living places. In Ireland fairies are associated with the pre-Celtic inhabitants of the island that were driven underground. Because they are so highly localized, when the people left those places, they left the fairies.

(Academic) Sources:

The Fairies in English Tradition and Literature by Katharine Briggs

The Fairy-Faith in Celtic Countries by W.Y. Evans-Wentz

I have a secondary question: what is "Elf School" that OP mentions?

Wow. The answers here are sublime and I cannot compete on such a large scale. Normally, even if I knew an answer to a question posted to this sub I wouldn't even try to answer because I know there are so many people here who can do it with much more grace and cited material then I could. This particular area is my only exception.

When it comes to most mythological creatures with their roots firmly planted in European beliefs and traditions there is actually a simple answer. Immigrants from these countries tended to believe that the particular creature of myth said to inhabit their homeland was just that, a species of their homeland. There are obvious exceptions, but when European based creatures of myth are added up they far outnumber the ones found in New World beliefs.

For instance, Irish Fairy Rings/Mounds. This phenomenon has a scientific answer in the form of a particular fungi. This fungi, although not native to the New World is found today on North American soil. Now in very recent history the Irish government actually halted the construction of an airport to divert it away from these rings because the superstition surrounding the bad luck they bring is so strong. Yet Irish American immigrants have rarely ever written or spoke of their thoughts in identical rings in N.A.. The fairies that cause these rings with their dances by the moonlight live in Ireland, not here (as far as they are concerned) and fungi rings here typically garnered no more then a glance. In fact fairies are such a deeply embedded belief in Ireland some surveys state that over 40% of people in Ireland claim to have seen a fairy while over 80% state their unwavering belief in the creatures.

Now one would gather that especially during the Great Famine and the massive influx of Irish people that this little creature of myth would 'come along' to the New World. However, it did not. The immigrants considered N. America "fairy free", because well fairies are Irish. This is not to say there have been no reported fairy sightings on American soil but when weighed against the vast Irish immigrant population they are very few. At least much fewer then had the same number of people in Ireland been surveyed on their sightings on home turf.

Now let's look at another creature of myth; gremlins. These creatures have dozens of different names and are acknowledged by several European cultures, but I'm just going to use the term "gremlin" for now. Germans were known to be fairly great believers in these creatures all the way thru WWII. Hitler himself ordered searches and rewards to anyone who could provide proof or even a specimen of one. It was all part of his bizarre occult obsession of course, as he offered up similar rewards for anything paranormal or cryptid in nature.

WWII German fighter pilots were known to be deathly superstitious of these troublesome creatures and often blamed malfunctions on their "dirty work". Different pilots (depending in what area of Germany they came from) had different "rituals" for ridding their plane of these nuisances. Some left sweets as an offering of peace, while others hid bits of herbs and plants gremlins were known to hate aboard their aircraft. German aviation mechanics were also quick to blame these creatures for any errors found.

Now during WWII this superstition briefly rubbed off on some British pilots and a small handful of accounts of German gremlin problems while on a mission were reported. For reasons I'm admittedly unaware of this belief amongst the Brits quickly died out.

The influx of Germans to America during and right after the war did help revive the belief here. German immigrants had brought their beliefs with them long before 1900 and many Americans saw the gremlins as vicious or evil gnomes that had been ousted from their community for some unknown sin. The 1930's-1950's saw a re-emergence of this creature on American soil and over that time period several dozen books were written (both fiction and reports of accounts) and reports of sightings were at an all time high. The reason this belief died out was pure survival. Many German immigrants wished to assimilate as quickly as possible due to the harsh feelings Americans had during and post-war. Many families altered their names and shed German traditions quite quickly in order to gain employment and avoid trouble in their new homes. This included leaving the idea of gremlins behind as well (even if they still believed it wasn't spoken of outside tight knit German-American communities). I will note that my knowledge of this particular subject (German gremlins) comes from familial first hand accounts and experiences.

For what it's worth, there are plenty of Central American folktales of diminutive, mischievous humanoids, often referred to as duendes in Spanish or another word in respective indigenous languages. However, many are likely based on Native American stories that existed pre-colonization.

Where I lived in Panama, there was a story about underground dwelling tiny humans called chambera in the Embera language, who live underground, are highly intelligent, had their feet on backwards, wear green loincloths, and come out at night to steal things and cause mischief.