This is a conjecture you put forward. It is on the same lines of let-them-eat-cake as:
> Generally, these workers, if they are willing to work hard and raise their skills, they will be able to increase their wages.
Sorry, but what evidence do you have that anything Trump has done has produced this result? Or even that this is the result of stemming immigration and not, say, steadily increasing demand in the economy?
In regards to the illegal immigration, other than the small bump due to people fleeing violence associated with Honduras, illegal immigration has been at a multi-decade low. Trump talks about it a lot, but this was already a substantially smaller contributor to labor markets when he came into office.
Meanwhile, the unemployment rate has been dropping quite steadily over the past decade - it didn't adjust dramatically as a result of some Trump-related policy. This is entirely the result of the end of the Great Recession, which kicked up unemployment by a huge percentage around the world. It's now basically recovered to its pre-recession levels. A decade of GDP growth is also bringing aggregate demand where it used to be.
These systemic factors seem much more likely to me to be responsible for this tight labor market than any kind of fiddling with immigration policy, whose effects would take years to feel if they could even produce this kind of change.
Since this is a forum with a lot of engineers I would expect people to do their research instead of simply making statements.
Exporting labor to cheaper countries (primarily China and Mexico) and importing cheap labor (through both legal and illegal immigration from low-income countries such as Mexico) and STEM imports through H1-B Visa abuses depresses wages for the working class in the former situation and among highly skilled professionals in the later.
There is a term for this: global labor arbitrage
Of course, there is a number of working class jobs replaced by automation, but in spite of automation, global labor arbitrage still exists as an independent phenomena to depress wages.
In 2001 China joined the World Trade Org (WTO) but "did not play by the rules." with the result that many Americans in working class jobs lost those jobs or ended up receiving depressed wage rates.
NAFTA has been an issue with Mexico.
The H1-B Visa abuse has been substantial with a number of organizations importing H1-B Visa labor to replace Americans (e.g. Disney, Southern CA Edison, UC San Francisco,...).
Trump has been working to stop illegal immigration as well as stemming H1-B Visa abuse. A result is that there are "labor shortages" resulting in a rising wage rate.
Another major factor impacting wage growth has been the increasing costs of healthcare which is generally paid for by employers. Higher benefits costs result in lower wages.
BTW, there are some companies that complain that they can't find workers but generally that is because 1) they are not offering market level wages and 2) they are not located in a place where people want to live.
Generally, these firms, if they are willing to locate where people want to live and if they offer market wages, they will be able to find employees.