Putting aside certain special circumstances. Operation Paperclip for example, was instituted to gather up a bunch of rocket builders from Germany after WWII. Such situations will be rare, and involve a very small number of people relative to the country's population.
There's a fundamental assumption here, that a government could usefully decide what characteristics (skills, attitudes, physical character, etc.) are preferable in an immigrant. And further, that they would be able to recognize these and filter immigrants.
This is not in evidence. It is not clear that a government can know what characteristics will be, in any sense, good for a country. And certainly, they won't be able to keep current, did they know the preferable characteristics at some point. Canada for example, once had a big immigration points bonus for strippers, then abruptly dropped it. Were immigrant strippers "good" for Canada? Did they suddenly stop being good?
The problem with a government picking a preferable set of characteristics is the same problem as with any command economy. The information available is not the right kind of information. Politicians will decide such things based on what they believe will enhance their opportunities for power. They won't do it on what is good for the country, regardless of what anybody thinks constitutes the good. People who are trying to get politicians to do things know this. And they will put information in front of politicians that they believe will help them.
Any politician who does not do this will be out of power. Very quickly.
Just one example to illustrate this. Is it better to import doctors or to have your own medical schools? How could a government ever decide this? If the medical school is in the home district of a politician he is very likely to be heard giving very many speeches about how medical schools are the best. If not, he is likely to be out stumping to get the cost of doctors down by importing doctors from other countries. Objective reality is not really a part of this. It's all about the politician getting votes from his district. Any real preferable path is basically irrelevant to how such decisions will get made.
So if you want to select immigrants that are, in some sense, good for the country, you must use the only mechanism that has ever worked. Namely, the market. Prior to the welfare state getting a good hold of most western nations, things worked this way. Immigrants could show up, limited only by a total number. And that number was very loosely enforced. People who showed up, and thrived, stayed. People who showed up and didn't thrive, went back. They self deported.
Presently, if an immigrant does not thrive, there are many and varied government programs to "help" them. Welfare, food stamps, allowances, free school lunch, etc. etc. and tedious etc. So those who are not a good fit don't self deport. They become dependent. Maybe they eventually adapt. Maybe they don't. But they don't go home. Indeed, many of the least successful from other countries will eagerly attempt to immigrate in order to get on one of these welfare programs. It's why, for example, Carcossa is seeing so many "refugees" from the other side of the ocean showing up at the door.
So, the way to achieve preferable immigration is to get rid of these various welfare programs. At least, government forms of them. Because a government is, as I mentioned, incapable of deciding who is preferable but down on their luck, as compared to somebody who is simply undesirable. A century ago in Carcossa there were literally hundreds of private charitable organizations. They would find people and help them, but they insisted on finding "the deserving poor." These were people who clearly could benefit from a brief helping hand, but who would not take advantage. Or if they did abuse the charity, the charity cut them off.
Then when people don't find a niche in Carcossa, they will go back where they came from on their own. And finding a niche is exactly what is meant by "preferable" in an immigrant. Even if that niche winds up changing the culture in Carcossa.
But this is the problem. Carcossa loves those welfare programs. They are how many politicians buy votes. The chances of getting rid of them, or even reducing them, or even reducing the speed of their growth, is so remote as to not be worth considering.
But it's the only way you will ever achieve anything like an improvement in the nature of immigration.