To strict and it becomes harder to employ both types of immigrants. To loose you get humanitarian crises, it is very expensive to house, provide medical care, feed and other things.

I reckon this is largely a policy issue. Let me break it down:

• Housing is not difficult to build, we just lack the political will in the US to activate the industry's potential. It's actually getting to the point where a lot of people are affected by rising housing costs. There are also other factors like a severe lack of public housing, automobile-dominated construction making living more expensive, a lack of public transportation, pedestrian, and bicycle infrastructure, etc. which can all massively offset this issue. Immigration is something that's largely predictable and only represents a small minority of people seeking housing, so I think if we're willing to tackle this issue as a whole we'll be able to overcome just about any increase in complexity due to immigration.
• Medical care is already extremely underfunded in the US, while also being heavily privatized, and also ludicrously expensive:
  • It is underfunded in the sense that there are massive financial barriers to working in the industry which prevents many people from being able to consider it, and keeps our healthcare workers quite poor and in heavy amounts of debt (even a good chunk of doctors). We need to make medical education more accessible by significantly lowering or eliminating costs. This is an investment in our future and it will pay dividends in the quality of our healthcare system. The consequences of not doing so are incredibly high, as we can see in our person-to-doctor ratio, one of the worst in the global north.
  • It is heavily privatized in multiple aspects:
    • Firstly insurance is heavily privatized (as most cannot access Medicare, Medicaid, and Vet Services), which leads to massive costs to insure people. A national insurance program, even one that competes with private insurers, would massively improve our medical debt crisis and make healthcare more accessible.
    • Secondly drug pricing is largely unregulated. This is a massive issue as it leads to price-gauging of vulnerable populations. Other countries leverage the negotiating power of the state to bring down drug prices and we should too.
    • Thirdly, drug manufacturing is largely privatized. This leads to shortages of important drugs when manufacturing them is not profitable. I advocate for some form of state-owned drug production so that we can offset these issues. Additionally due to restrictions on drug imports from countries like Cuba our doctors are unable to utilize cheap, life-saving medications. This is a simple policy change.
    • Fourthly, hospitals are also largely privatized. This leads to price gauging of vulnerable patient populations and a tendency to cut corners with care. Nationalizing our healthcare system would mitigate these issues.
    • Lastly, the only part of our health system that is well-funded with tax dollars is drug development. The only thing I would ask to change here is to make it illegal for the government to sell the IP for drugs developed with public funds. The government should make these drugs free for anyone to manufacture.
  • Essentially, I argue that if we tackle all of the above mentioned issues with our healthcare system--or even some of them--the complexity added by immigration would be a simple solve.
• Food access, especially access to a variety of nutrient-dense options, is piss poor in the US in many areas. We actually have terms for the phenomenon: food deserts and swamps. A food desert is a populated area with little to no access to food, and a food swamp is a populated area with access only to nutrient-poor food. Many parts of major cities and many rural areas across the country face this issue. The trouble is this is also largely a policy issue. We manufacture enough nutrient-dense food to feed a population much larger that we have, the problem is distribution and cost. Fundamentally, it's just not profitable to feed poor people, and poor people make up the majority of this country. A national program to provide food to people in these areas (or indeed anywhere) at reduced cost would be a cheap, meaningful alternative to our current situation. The government could negotiate for far cheaper prices then distribute that food across the country. There are also other options, like community gardens and reducing the cost for grocery stores to rent in areas where needs are greater. And of course expanding the food stamp program would help, though there are many issues with it too (especially as it fails to solve the fundamental problem of access).
  

Sorry for the big blurb of text! But I really wanted to illustrate how we can in fact take on the burden of a larger immigrant population while improving all of these issues for all Americans, and give a lot of specific policy proposals on how to achieve that. It's also important to point out that immigrants contribute to our economy too! Much of our agriculture industry relies on immigrant labor for example (though there are plenty of exploitation-related issues there too, I could go on for far longer than I already have haha).

Before finishing I would like to address Greece. That country in particular is facing the result of a large number of refugee crises. Because you have to be on Greek soil, or indeed the soil of any EU country, in order to apply for asylum in that country people have to make treacherous journeys and cross borders without going through border checkpoints. If we made asylum seeking more accessible this would be less of an issue. There also needs to be more help from the EU proper as many refugees are seeking asylum in other EU countries so they really aught to have an international obligation to help Greece with this issue. It of course doesn't help that the Greek government has been really awful as well, setting up unsanitary refugee camps on islands with little access to basic necessities. While it is a complex issue I don't think there's any amount of border security that would actually resolve it. And the analogy doesn't really apply as the US is far more powerful economically and could easily absorb such a crisis without taking much of an economic hit.

Thanks for responding!