And yet, for a long time in the past century, the U.S. dealt with a massive influx of immigration from all around the world, with all of the complications around culture, resource, and education that you mention. But it seems to me that it is one of the chief sources of the country's strength, no?
Yes, and you still had to present yourself at the border, with a passport, and be registered. Controlling immigration doesn't mean preventing people to get in, it means knowing who is coming in, and how many people, at which rate, so you can take decisions.
Besides, while it is a country strength, it did and still do have a cost. Whether this cost is worth the benefit is something you can only answer if you have metrics to do so, and illegal immigration make it hard to have those metrics, or change your policy to adapt to your new situation.
People always see immigrations as being a moral issue first, but it really is not. It has strong moral implications by nature, but it's first a management issue. Just like eduction, science, etc.
For a long time in the past century, the US didn't have any safety net. So whosoever came here essentially had to bootstrap themselves.
I believe you can have only one of the two - open borders, or social safety net. Having completely open borders with generous social safety net is mathematically impossible, unless you want to discriminate against the newcomers by denying them the benefits (which is, again, a bad thing according to many people).
