This doesn't take into account all the legal immigrants such as my grandparents who came to this country, and perhaps yours, to escape tyranny. Many legal immigrants have excellent educations and/or skills that continue to enrich our societies.
You don't need to be so cynical.
I am from the UK, not the USA.
Only my mother is a recent immigrant, as she is Kosovan Albanian, while my father is English.
Its not a case of people not enriching the Countries they go to, many do, but its a case of how in a worldwide, free market economy, immigration is used as a tool and form of exploitation, many immigrants are desperate and move for economic reasons, often due to the lesser living conditions in home nations, they accept less than the going rate for skilled work, so then the wages for everybody take a hit, as the wages are undercut.
That's the reality of it, its an important part of the economic reality of greedy and exploitative world we live in.
For example, imagine if you worked in a Trade where the "going rate", with shift rates, etc was £25 an hour, then a group of people turn up who are willing to do the same job for £12 and hour, that's it, you yourself now have to accept £12 or you won't get the job, so your wage has been cut in half for using the same skill set, nobody is happy about that.
But what they do is then blame the wrong people, they blame the immigrants themselves.
The reality is not to ban immigration however, but to Unionise all workers and the migrants join the Unions, then the migrant also works for £25 an hour as well, which they would be happier about as they'd be being payed more.
You see in history, the answers presented for this problem have been either Nationalism, as in to stop immigration altogether or Internationalism, as in to unite all workers and peoples to a common cause so they won't undermine each other but are still free to migrate to other places. The former, Nationalism can stagnate and isolate a Nation in the modern world and turn its people against other people for National identity, while the latter, while hard to make work, would be a better alternative and a way in which to take a hammer to the foundations of exploitation worldwide.