I return to the question of whether immigration affects the wages of U.S. born workers. The short answer is that academic studies for the U.S. and other countries tend to report little impact. And, some careful mental speculation would come to the same conclusion.
This may well have to do with how immigration works in advanced countries, with relatively little size of immigrant workforces vs the existing workforce, and the fluidity of the workforce of an advanced economy. (Thus, large numbers of Venezuelans rapidly migrating to Columbia may well affect wages).
A 2011 meta-analysis with 213 citations concluded that “the likelihood and magnitude of adverse labor market affects for natives from immigration are substantially weaker than perceived. Most studies find only minor displacement afterwards, even after very large immigration flows.”
The question of wage effect may be the wrong question to ask in an advanced economy. A better question may be, does immigration increase or decrease the number of Americans employed, leaving aside wage impact. In an environment of labor shortage and a dynamic economy, immigrants may both increase employment and wages. But the effects will almost certainly by very local.
Jobs for persons with a lot of formal education. Some studied (and your own speculation) suggest that medical doctors, computer scientists and other education immigrants may in fact increase the numbers of U.S. born persons employed (their wages may not go up). Consider the immigrant who provides a critically needed expertise to a team.
Jobs for persons with low formal education. Consider persons without a high school degree. 26% of all immigrants have less than a high school degree education compared to 8% of U.S. born persons. (This high rate for immigrants has almost certainly gone down among recent immigrants.)
Divide the jobs between those requiring or favoring English proficiency and American cultural literary (Type A) and those not (Type B). Type A: restaurant server, barista, sales staff in retail. Note that these jobs involve a high level of social interaction and opportunities for self-expression. Type B: landscape worker, warehouse worker, farm worker, waste management, semi-skilled factory work. Note that these jobs effectively preclude the worker from expanding her use of English and interacting with the public. Consider that many of the Type B jobs are relatively very hard, such as meat processing workers. We can infer that in a dynamic large economy poorly educated immigrants do not necessarily compete with their peers in education.
Also go here.