It is important to look at facts. I just googled "nations with open borders" and chose these citations from the many links offered. As this is a forum for Objectivists, allow me to suggest a cautionary argument from Understanding Objectivism by Leonard Peikoff and Harry Binwanger. Answering a student's question, Peikoff warned against "monism" attempting to derive all truths from A is A by pure logic. Answering another question about the hierarchy of knowledge, Peikoff said that you cannot make metaphysics antecedent to epistemology: reason and reality must always be tied to each other. So, too, here I point out that Harry Binswanger's article cited at the top does describe the United States of the near-capitalist 19th century, We had open borders. We also defended our national sovereignty against the United Kingdom (and lesser threats). Similarly, living as I do in Texas, when we were a republic, we declared and then defended our sovereignty in part specifically to have open immigration.
"Pervasive international border control is a relatively recent phenomenon in world history. In the past, many states had open international borders either in practice or due to a lack of any legal restriction. Many authors, such as John Maynard Keynes, have identified the early 20th century and particularly World War I as the point when such controls became common.  Keynes, John Maynard (1920). "2". The Economic Consequences of the Peace. New York: Harcourt Brace."
Uniquely, the Norwegian special territory of Svalbard is an entirely visa-free zone. No person requires a visa or residence permit and anyone may live and work in Svalbard indefinitely, regardless of citizenship. The Svalbard Treaty grants treaty nationals equal right of abode as Norwegian nationals. So far, non-treaty nationals have been admitted visa-free as well. "Regulations concerning rejection and expulsion from Svalbard" are in force on a non-discriminatory basis. Grounds for exclusion include lack of means of support, and violation of laws or regulations. Same-day visa-free transit at Oslo Airport is possible when travelling on non-stop flights to Svalbard.
 "Entry and residence". Governor of Svalbard. Governor of Svalbard. Retrieved 20 June 2016.
 "Immigrants warmly welcomed". www.aljazeera.com.
Wikipedia here: https://en.wikipedia.org/wiki/Open_border
A Harsh Climate Calls for Banishment of the Needy
The key to Svalbard’s status as probably Europe’s closest thing to a crime-free society, according to the governor, is that unemployment is in effect illegal. “If you don’t have a job, you can’t live here,” Mr. Ingero said, noting that the jobless are swiftly deported. Retirees are sent away, too, unless they can prove they have sufficient means to support themselves.
Although governed by Norway, a country that prides itself on offering cradle-to-grave state support for its needy citizens, Svalbard, an archipelago of islands in the high Arctic, embraces a model that is closer to the vision of Ayn Rand than the Scandinavian norm of generous welfare protection.Even Longyearbyen’s socialist mayor, Christin Kristoffersen, a member of the Labour Party, wants the town — named after an American industrialist, John Munro Longyear, who founded it in 1906 — to stay off limits to all but the able-bodied and gainfully employed. https://www.nytimes.com/2014/07/10/world/europe/a-harsh-climate-calls-for-banishment-of-the-needy.html
How Open Borders Died in Five Countries
By Bryan Caplan
This is a summary from a free market perspective of this journal article:
"Immigration Policy Prior to the 1930s: Labor Markets, Policy Interactions, and Globalization Backlash" by Ashley S. Timmer and Jeffrey G. Williams
Population and Development Review
Vol. 24, No. 4 (Dec., 1998), pp. 739-771
The Case for Immigation
IN HIS novel “Exit West”, Mohsin Hamid describes a world very like our own, but which is suddenly changed by the appearance of mysterious doors. A dark-skinned man falls out of an Australian woman’s wardrobe in Sydney. Filipino women emerge from the back door of a bar into the alleyways of Tokyo. As the incidents multiply and scores of people from poor countries walk through the doors into richer ones, rich-world inhabitants respond with violent resistance. Governments crack down hard on the new arrivals. But it is not long before they are overwhelmed by their sheer number and abandon efforts to repel them. The world settles into an uneasy new equilibrium. Shantytowns emerge on the slopes of San Francisco Bay. Conflicts in war-torn places burn out for want of civilians to kill and exploit.
Mr Hamid’s story comes close to what many advocates of open borders believe the world would look like if people were free to move wherever they wanted: fairer, freer, with more opportunities for a larger number of people. But it also nods to the fears many people have about unfettered migration: uncertainty, disorder, violence. Would such a world be a dream or a nightmare? The answer depends on whom you ask.
Citizenship is a different question. Ultimately, in the United States, citizenship meant the right to vote and the concomitant rights to serve on a jury and be elected to public office. However, non-citizens were nonetheless accorded trial by jury, freedom of religion, etc., and millions of non-citizens served in the armed forces of the United States.