I actually read through two of the "proper economic analyses" in that reddit link since I am interested in this.
One of them wasn't an economic analysis but a summary article: https://www.migrationpolicy.org/research/contributions-high-.... Almost all of this article is talking about all of the problems with trying to identify the net effects of immigration and how difficult it is.
It has quotes that directly refute what you are saying such as:
"Immigration has complex, sometimes ambiguous impacts on natives. The benefits to the US economy from high-skilled immigration can be accompanied by negative effects for certain groups of natives and positive effects for other groups." Which is the opening summary of the section on effect on natives. Also,
"Borjas found that a 10 percent increase of immigrants with PhDs in a certain field lowered the wages of native born graduating with doctorates in those same fields around the same time by 3 percent"
"Researchers have also examined the degree to which high inflows of foreign-born students affect the educational opportunities of native students. Borjas finds some evidence that an inflow of foreign-born students displaces native, white male students in elite institutions"
The other main article https://www.ppic.org/content/pubs/cacounts/CC_207GPCC.pdf is more positive but there is no way you can call it a rosey picture.
Clearly, the biggest effect of immigration is on previous immigrants (currently 30% of California): "Foreign-born workers already here sustain the largest losses in real wages, losing between 17 and 20 percent of their real wage over 14 years."
It just so happens that natives (specifically who are college educated) tend to have complimentary skill sets in the years mentioned.
"Except for workers with some college education, whose real wage gain is around 6 to 7 percent, no other group experiences real wage gains or losses larger than 4 percent. This implies that even with the moderate costs of moving, in the range of 5 to 10 percent of their yearly income, native workers would not move (out of or into California) in response to immigration."
That is the support you have that "native-born workers benefit from immigration". It helped college educated natives and the rest of the population wasn't negatively affected enough to leave California. And that's based on migration data ending in 2004 and Californians have been leaving in record droves since then.
Of course, it doesn't mention any thing about the rest of the effect on natives such as cost of living increases due to crowding, strain on institutions (do you want to send your kids to an average California school?), unwanted changes in culture and politics, decrease in social cohesion, decreases (or lack of improvement) in working conditions, increases in inequality or any of the other consequences.
The average US male wage has barely moved since the 1970s during a time of unprecedented levels of immigration. If immigration is such a net benefit to native-born worker, where did those improvements go?