Indeed so- in fact, here in central Texas, there are a lot of people who still speak Czech, even though their families came here more than 150 years ago.
I think you’re letting your personal biases ruin the narrative. I think it’s always been true the vast majority of people would rather remain where they are than move. Familiar for most people will almost always outrank other concerns. This is why the Deep South still has the states with the largest black populations, because despite the history of slavery, the generations of discrimination and the crushing poverty for most black Americans “home” is where they were born and most people like to stay around home. The “great migration” North is even similar to European immigration to the New World–yes, it happened, but obviously it was never a majority movement, it was a small subset who were willing to uproot their lives for the chance of better ones (with mixed results, as you might expect.)
This question is actually not as sensible as you might presume, if only because the answer is basically “read a book on the history of the New World c. 1492-19xx.” The reasons have always been numerous.
The reasons also give you different types of immigrants. Since Germany was a fractured collection of principalities and often the battleground for major European wars in the first part of the 19th century, many Germans who immigrated to America were not actually that poor. Instead, they were more like the successful farmer class who wanted to get away from all of the wars. This is also why they didn’t tend to settle in the major cities and start looking for blue collar work to the same degree as the Irish and Italian immigrants. They had money and resources to setup farms for themselves (and know how as they had been farmers back home.)
Religious separatists often weren’t necessarily poor, but were willing to leave to avoid troubles back home. The French Huguenots that came to America for example, as a rule had some amount of money.
Asian immigration on the other hand has almost always been about economic opportunity (with a spike from Vietnam due to our program which let refugees of the war into the United States until 1990 or so.)
It’s also not really true it’s a “myth” that much of the world has some desire to live in America…yes, “America” specifically is a myth, but many people in the developing world have some level of desire to live in the first world. Not typically enough to actually act on it, and many who have enough desire to act on it don’t have the means, but there’s a reason people from the developing world are clamoring to get into the United States, Canada and the E.U. states and only immigration controls keep the numbers from being much higher.
And now I want a kolache and a pilsener. 
If you saw my last name, you’d assume my grandmother came from Venice. Nope, she lived near Rome.
So much so that after the explosion in West, TX, the Czech Republic made a donation to help rebuild.
What about Spanish or Portuguese? AFAIK, you don’t see a lot of immigrants from those countries.
Eastern Europe seems to be the biggest group in my neck of the woods, along with the Irish.
I don’t know about Spain but there is a sizable Portuguese immigrant community in the U.S.
A lot of Portugese went to Hawaii (where they served as the butt of jokes normally filled by Poles on the mainland. Wait - that doesn’t sound quite right.)
The US receives a lot of immigrants from the UK. So many that UK citizens are not eligible to enter the Visa lottery (aka Diversification Visa) because the UK already sends more than 50,000 immigrants per year to the US.
Back when I used to read the Guinness Book of World Records it had a section on immigration and emigration. The US always held the record for receiving the most immigrants in all the years I read it. The record for the highest number of emigrants alternated between the UK and Mexico. I haven’t read that book for several years now though.
And yet more Brits still emigrate to Australia, and almost as many move to Spain.
A lot of immigrants whose ancestors were originally from those countries are “secondary immigration”, they reach the US as Mexicans, Costa Ricans, Peruvians, Brazilians…
My American university’s Spanish students club had just been started the previous year (we’re not fond of official clubs, but getting the paperwork done meant being able to schedule rooms much more easily than as individual students); it was already the second-biggest. Second-biggest group of foreign students, as well, after the Cubans… speaking of whom, you would have thought that half of Catalonia and three-quarters of the Canaries had grown cane at some point: every Cuban-American my age I met had at least one great-grandparent from each place, every one my parent’s age at least one of either. And did I ever tell you guys about meeting a long-lost cousin of my father Over There, and finding that her brothers had also moved from Venezuela to the US? They’d moved to Venezuela as little chidren, acquired Venezuelan nationality, then moved to the US as adults and acquired American nationality.
Nava, but that is what happened. People from those places where some of the major immigrants to Cuba and Puerto Rico in the first half of the nineteenth century. I’m going by roughly the dates, but around 1815-1830 is when people from the Canary islands and Catalonia started coming to the islands. Granted, this is also when a lot of the other Latin American countries were independent or in the way to independence. The Real Cédula de Gracias is also what brought immigrants from non-Spanish countries to Cuba and Puerto Rico.
And yes, my European ancestors came mostly from Mallorca and non-Spanish speaking countries.
Also, they didn’t grew cane necessarily, unless you mean “they owned the plantations”. They grew other things like coffee, and were mechants and small landowners.
OK, I know I learned this in my history classes, but here is a quick wiki link (in Spanish).
Well, I’m reasonably sure that while there was a ton of people who went to Cuba from Catalonia and the Canary Islands, it wasn’t quiiiiiiite half of one and three-quarters of the other 
Just a little less. And while I know people whose relatives emigrated to Cuba from other parts of Spain, somehow they all got eaten by a sea monster on the way or something - you never meet a Cuban who tells you “hey, my greatgrandpa was from Tarazona! Do you know Tarazona?”
But yea, the main point of my post was that there is a lot of people in the US who have lots of Spanish blood by way of the rest of the former Spanish colonies and others with Portuguese blood who reached the US by way of Brazil.
Unless they’re from Northern Ireland.
Often featured on Family Guy.
French too, most of the Americans I know who are of French descent are French by way of Canada, i.e. Quebecois and Acadien.
I’ve heard of this - that the US considers Northern Ireland a separate jurisdiction when it comes to granting immigration visas. Can a UK citizen from somewhere else move to NI for X number of years in order to “become Northern Irish” enough for the US to consider them as such? Is it a fixed number of years or does the US do a whole person analysis to determine how much they have assimilated into a Northern Irish lifestyle? (e.g. adopting a local accent and/or dialect, taking part in community activities, marrying a Northern Irish person, voting in NI elections, being accepted as Northern Irish by community members, etc.)
I seem to recall reading that Spain considers Puerto Ricans to be eligible to immigrate to Spain as former colonials, and that Puerto Rican citizenship is granted de jure to US citizens for living there for X number of years, and that is theoretically be a backdoor way for Americans to move to Europe. No visa to move to PR, X years there, then apply to Spain as a Puerto Rican.
Where did you get the idea that we Yanks think EVERYBODY wants to come here?
Historically, millions of people from MANY countries HAVE come here, but even the most patriotic American knows that MOST people don’t want to leave their homes and families and travel halfway around the world. It goes without saying that MOST people would prefer to stay close to home if they can make a decent living. That was true of my Irish grandparents, and it’s true of young Chinese and Indian engineers.
Times and conditions change. In the 19th century, large numbers of Swedes and GErmans came to America to establish farms and live better lives. Today, Sweden and Germany are very prosperous countries, so few Swedes or Germans have much incentive to come here. We understand that!
The Celtic Tiger isn’t quite what it was a decade ago, but Ireland is still a much richer country than it was. Decades ago, an ambitious young Irishman almost HAD to leave home. Today, he DOESN’T have to. We understand that, and don’t expect young Irishmen to flock to America as they once did.
AFAIK there is no law granting special rights to “former colonials”, but IANAL. Sadly a search of the webpage of the Secretaría General de Inmigración y Emigración hasn’t yielded anything specific on the subject other than confirming the existence of specific treaties between Spain and several of her former colonies (no blanket law or multi-party treaty covering all of them that I can find) and the complete lack of a “contact us” form. No specific migration treaty between the US and Spain.
Something I do know applies to many people from former colonies (but not because of being from one) is the “emigrant return” rules, which give to the children or grandchildren of emigrants the right to petition for Spanish nationality sort of as if their (grand)parents had actually bothered/been able to register their births at the appropriate consular office. That would apply to my cousins in Vermont without any kind of need to move to Puerto Rico, what they would have to do is prove that their maternal grandparents were from Spain (it would work for only one, but in their specific case it was both). Italy has similar rules; along with the language similarity, this helps make them a favored immigration country for Latin Americans into Europe.
New Bedford, Massacusetts, used to have the biggest Portugese community in the USA (maybe they still do). Famed chef Emeril Lagasse is the son of a Portugese mother and a French-Canadian Dad, and grew up in New Bedford.