Well, that's an important point. A large part of our population is only able to handle low-skill work. But we don't need them -- so what happens to them?
There is a huge shortage of workers -— highly skilled ones -— in the U.S. It is somewhat filled by H1B program, but that is a drop in the bucket.
Well, we wouldn't have such a shortage if these highly skilled jobs actually paid well. And why don't they pay well? In part, because H1B's undercut the salary that would otherwise be offered.
Technical work is difficult, requires a constant effort to stay informed on the latest advances, and carries a real fear of age discrimination. It's tough to convince people to go into these fields. Better pay would help, but if we import cheaper labor, then the pay doesn't rise appropriately.
There are a great many 50+ engineers walking around looking for work. But people talk about a shortage of highly skilled workers. This isn't about skills; this is about money. We don't want to pay for highly skilled workers.
The same thing as happened throughout our history. We constantly learn (from the market) what skills are needed and what they are worth. A significant shortage of programmers, which lasted from 1960s until recently, was signaled by very high salaries (compared to education level), and attracted great many people into that profession. When shortages subsided, salaries and job openings fell.
What impedes/amplifies that process are cultural traits, reflected in part in the education polices pursued. After the Russian scare of 1950s, it was very respectable to be a scientist and engineer: you protected the country by strengthening our military, and prolongs and improved lives by new drugs, conveniences, etc.
It's been too long now. Most people take those benefits for granted. It is not "cool" to know mathematics and physics --- in fact, that will reduce the number of dates you get. Our education policies --- the dumbing down of our nation for several decades --- result in a devaluation of our college degrees (how many remedial, high-school level classes to students take in college now?). The size of a teenager's vocabulary is one half of what it was in 1950s. He still gets a high-school or college degree. All this gives an erroneous impression about the competitiveness of our labor force. Our prosperity, in turn, gives an impression that you can do well without being good. Forces such as these render changes in labor very slow.
"Well, we wouldn't have such a shortage if these highly skilled jobs actually paid well."
That is a common but an erroneous argument, based on misunderstanding of economics.
The first problem is looking at the labor market in isolation. It is connected, however, to the product market. Suppose you can sell a product for no more than $10 and require a certain skill to create it. You need to workers and found one, paying him $9.90. No other people want to work at that salary. Will you offer a salary of $10.10. Of course not: the whole point of employment becomes moot, because you'd be incrurrng a loss at that salary.
Second, and perhaps more subtle error, is in the belief that price always adjusts to demand. That is what you indeed learn in economics. What people forget, however, that this is not universal: such thinking applies only to where there is no rationing (shortages).
To make the point simple, suppose you want to hire Einstein. Princeton got him. Suppose they paid him $200,000. Now you are looking for another Einstein. Suppose you are willing to pay $500,000. How many Einsteins will you get? None, of course. Well, you increase the salary to $1,000,000. How many will you get now. Sill none, of course. Why? Because there aren't any more Ensteins. Given the shortage of Einsteins, no increase in salary will help. Companies are not looking for Einsteins literally, but this illustrates the point.