Sowell goes over a massive portion of this in his works on "Immigrations And Cultures"

In the later part of the book he goes over the fact that Immigration actually has a massive effect on the economy, and that if you accept migrants from places that are already safe, successful, prosperous, and close to your own cultures values, you can actually have very beneficial immigrant communities IF AND ONLY IF the domestic population doesn't suffer from the politics of resentment which then generate internal strife.

To give you a specific example, a large wave of migration from Rural Ireland into South Korea is probably going to be a bad idea because Rural Irish and Korean cultures are wildly different, and would cause the Irish to segregate themselves off. Whether or not they will succeed in Korea would be irrelevant because they might always be seen as foreigners allowing resentment to be generated.

If you take Irish Immigrants only from the high paying tech scene of Dublin, they might integrate economically into the Korean society. They may even cause the Korean society to prosper due to innovations taken from the Dublin Silicon Valley Scene explicitly. However, this doesn't get you past all potential problems. Resentment can still be stoked if your Irish immigrants start being more successful than the general population. This is -NOT- resolved by trying to lay down political policy to help bring up the domestic population to the level of the immigrants. Even a genuine attitude of Noblesse Oblige by the successful immigrant group can still stoke resentment.

Whether your immigrants are rich or poor, privileged or oppressed, if the politics of resentment get involved, it's gonna be a bad time for everyone. So they have to be integrated and assimilated into the population.

Big emphasis: this is not replicable from poor parts of Dublin, the differences in immigration outcome may vary by the street and only from that given time. Immigrant groups tend to act like time capsules from the exact moment in time & space where they come from. They will repeat that culture, possibly for generations, even if the culture they came from changed and no longer represents it.

He makes it clear that immigration was often the only way for new innovations, mechanisms, procedures, cultural traditions, and technologies to reliably enter into a different society for most of history. However, he's mentioned that the existence of foreign corporations actually now allow for the benefits of such things to be bureaucratically implemented within the corporation, which may allow domestic competitors to learn and adapt those mechanisms for themselves. They DON'T have to actually facilitate large scale foreign migration.

There a whole chapter on why successful immigrants tend to be nepotistic, and it is related to social cohesion and a knowledge filter, but it's too long to get into unless you want it in a reply, so let's just leave it as: successful immigrant groups will appear nepotistic due to working social.

So, knowing that, here's trade off with immigration. I'll give the steel man trade offs for both immigration and anti-immigration, and the pre-requisites involved:

• A good, working, immigration system allows you to benefit from narrowly tailored populations who are explicitly socially cohesive and integrous in ways that your own culture and society is not familiar with. If you are unwilling to import the immigrants themselves, allowing a foreign corporations to employ domestic workers can also do the trick.

This assumes you will be correctly tailor your migrants carefully. You CAN NOT take them from resentful, angry, violent, incestuous, or incompatible places. You WILL bring their culture, even if it is initially only. It also assumes that there are social and cultural problems in your society you are not able to work around. It also requires you integrate these immigrant populations into your society. You MUST prevent the politics of resentment from developing around BOTH the domestic and immigrant group, regardless of the actual economic outcome of that group, or there will be violence. Any social cohesion problems already present in the domestic society will not be solved by this, and must be solved independently. A corporation introduces new problems, and begs the question if whether or not that corporation is truly benefiting your society, and if it's employees are actually getting the benefits of the foreigner that you were hoping. Looking at these requirements, your regulations have to be very strict to make sure you have positive outcomes. You have to be about as careful with this as a major corporate merger. You can't just let anyone in.

• A strong anti-immigrant system sees no need to benefit the society with the difficulties of assimilating immigrants and cultures into it's own. Fundamentally, the anti-immigrant society sees no benefits in immigration and appears to be the creation of an unnecessary problem.

This assumes you already are at the top of your game as a society: that there's nothing to actually improve and everything is as efficient and prosperous as it could possibly be without exception and there are no other challenges on the horizon, even to the point of geopolitical threat. Unfortunately, it means that such a position is almost universally wrong except when attached to the world hegemon at the peak of their power. Even in the event that you think that you've got everything worked out, you probably don't. Ideas from other places that work could work in your domestic country but you don't even know them. You are assuming that there is no potential success, but we know in history that this is almost never the case, and a society that takes in no migration inevitably is unable to adapt or evolve in the face of new and emerging problems.

For my opinion, I think immigration is still good, so long as strict as if we were head-hunting for top tier employees and communities, and you have to recognize that assimilation will take a minimum of 3 generations, and you have to basically prevent immigrants from setting up immigrant communities. This is quite hard, and is why you need to have very low migration. 1% of your current population might be the absolute max of what you can actually afford.