Ok I see what you are trying to say. However, counterpoint is why do you call African-Americans that instead of Americans? Aren't we all Americans? I don't see you saying Polish-Americans or such when referring to them.
If you think referring to illegal immigrants is wrong, then do you think you are wrong when you say African-Americans?
Why do you say violent criminals for violent offenders? Why not just criminals. Why do you say criminals for people who broke the law in America? Why not just Americans. Why do you say Americans for humans in America? Why not just Humans?
Your argument doesn't really hold water.
Unless you specifically just call everything the same thing then what is really your point?
The Human shot the human the other day while at the Humans Days Festival because another Human from Planet Earth was badgering the Human and his Human pals because the Human was of Human descent.
There are immigrants and a subset of immigrants who have done so illegally. If you are trying to stress you are only referring to legal immigrants you could point that out to clear any confusion. Why doesn't the word legals exist? Because it is already covered by immigrants. The expectation of immigrants is that they are of legal status. Hence the qualifier if not.