Foreign occupiers of a host nation unlike those born in the host nation are generally there on the goodwill of the host nation. It is important to remember that a host country has no obligation to its foreign citizens other than universal rights. Therefore immigrants generally cannot complain about immigration policies, however dumb or immoral they appear to be. Accepting this, immigration policies can still be designed in a way that is highly beneficial to the host nation. The immigration goals of most countries are to expand the labour force. This can be a good deal for countries as they can get an above average addition to the labour force without having spent the money to educate them. Certain countries are known for being difficult countries to become a citizen in: Switzerland and Japan come to mind.
But citizenship is only a subset of immigration. Citizenship is a symbiotic relationship where the country becomes obliged to offer the foreign citizen the same rights as it does its natural citizens. Even Switzerland and Japan are very happy to have foreign workers to expand their labour force, especially if the countries offer nothing in return. There is rarely a good argument to not allow a foreign citizen to pay the government a lot of taxes, when the government has no obligations back to the foreign citizen. One argument is that foreign workers take the jobs of domestic workers. That is not true, and there is even a fallacy named after it. The Lump of Labour fallacy is to assume that the labour market is zero-sum - that one person being allowed to work precludes another. When women entered the labour force, there was no appreciable increase in unemployment. Governments are actively increasing the retirement age, not lowering it. And very few economists would think that reducing the hours of a work week is sound economic policy. By the same logic, immigration does not necessarily result in increased unemployment. And where supply of labor does not increase more than its demand, we do not need to worry about wages. Certainly, wages for a certain class may fall a bit, the wages for the average citizen will not be affected.
Using this as a theoretical base, governments therefore only need to at least compare the taxes it will receive from the citizen with the cost the citizen will cost for the nation. With the progressive way taxation works, a foreign citizen with an average equal to a domestic citizen will not contribute much in taxes at all (<$10k). Here the cost/benefit for the government is not entirely clear. One can argue that given the US is perpetually in deficit, that the average citizen is a negative contributor. Then again, the foreign citizen will not benefit from healthcare and social security. This is not to say that we cannot have immigration beyond this criteria, but at least this criteria seems grounded in indisputable logic.
Then there seems very little incentive for countries to put any limit on foreign citizens who want to work and given they pay taxes above a certain threshold the government deems to be acceptable. As such most nations around the world have very lax policies when it comes to allowing foreign citizens to work.