I agree that this is an oversight. It's all well and good to say that "the economy is larger by $200B because of illegal immigrants, and functionally more wealthy by $100B (or whatever it really is)", but as you say, it doesn't tell the whole story.
I have very little respect, intellectually, for the supposed liberal who claims to be supportive of illegal immigrants living in the U.S. while taking actions that completely shield themselves from the downsides that some people feel due to increased competition, and/or the downsides felt by the illegal immigrants themselves due to their illegal status.
But I think it's important to separate two sides of the problem: (1) illegality, and (2) increased competition for a certain class of typically low-income jobs. Right now, our immigration policy is formally restrictive but actually pretty lax, causing a situation where the two are conflated. But if we were formally lax, illegality problems would basically all go away, while the increased competition might even get worse (or it might get a little better but only a little because unscrupulous businesses couldn't take advantage of legal immigrants the same way they can take advantage of illegal immigrants).
The costs explained by your articles aren't wrong, exactly, but they don't do a good enough job looking at the whole picture. For instance, everyone pays more for health care when hospitals have to cover the cost of (very expensive) emergency service for people who can't pay and probably wouldn't have been there if they had proper health care earlier. This does tend to be more painful for lower-income Americans who are more likely to be uninsured or underinsured (though "Obamacare" has improved the situation quite a bit). But this would be mostly fixed by simply making immigration much easier--the costs are mostly due to the poor care leading up to an emergency. (This is true more generally of poor Americans without adequate healthcare--because they "can't afford" healthcare, everyone ends up paying more for healthcare for them and they end up less healthy, which is kind of crazy.)
There's the wage-depression issue, too. On the other hand, illegal immigrants tend to work in a lot of jobs that produce goods and services most needed by low-income individuals. For instance, we have a net subsidy of produce--fruits and vegetables--due to the widespread use of illegal immigrants to tend and harvest crops, and these things are particularly important to health and already are sometimes harder to afford (due to low calories/dollar) for low-income individuals and households. So illegal immigration in practice makes healthy food options considerably more accessible to low-income residents. The wealthy aren't helped; they could afford it if it was twice as expensive. If immigration policy became more lax, these issues wouldn't change.
Anyway, I agree that upper classes don't care much about the issues. My sense, as I've argued before, is that even in cases where the issues are made more acute by immigration, there are serious underlying problems anyway that need fixing. So in that sense an opposition to immigration and illegal immigrants is something of a red herring.
I would like to see the systemic problems fixed first and then, when we have better social mobility, less elitist funding of schools, and so on, come back and figure out what a sane immigration policy looks like. Those things that are legitimately costs right now may not be into the future. Yes, some of them might still be short-term costs, but that's why we have government debt: so we can amortize short-term costs in cases where we'll have long-term gain; to turn a problem into an investment. I think we have a lot of opportunity for that.
In the meantime, I think it's good to acknowledge that it's a highly complex issue, and that the "obvious" truths and costs are often not so obvious after all, because in most cases people are most impacted by the economy as a whole, not stresses in small portions of the economy.