When you follow the links, they say a lot less than you want them to. The Spenkuch study explicitly says it makes no attempt to distinguish between legal and illegal immigration. It looks at data from 1980-2000 and tries to find correlations between FBI compiled rates of crime by county and census data on the percentage of population self-reporting as immigrants. It found a small positive correlation for the rate of property crime. In the link you supplied it says
Spenkuch did discover a modest positive correlation between immigration and property crime, although this effect is only present with regard to “immigrants with the poorest labor market outcome,” he says, such as those from Mexico.
So the “well-established” “no correlation” is not supported by your own link.
Even more basic is the question of whether the relative lack of criminality of Cuban, Hungarian, Czechoslovakian, Soviet Jewish, Vietnamese, and other legal immigrants from 1950-1990 and who were subject to screening would also be true for the illegal unscreened immigrants from Mexico and Central America arriving in the last 5 years.
Part of the question is whether the decline in US crime since the 90s extrapolates to crime committed by illegal immigrants. If the rate of crime by immigrants is at the level it was during the 1980s, it would be quite a bit higher than the current average. It is an unsupported assumption that crime by immigrants will decline with the US decline. Some of those immigrants come from countries with higher rates of crime and from countries with increasing rates of violent crime.
Also, illegal immigration is inexorably tied to gang and drug cartel enterprises from drug trafficking and human sex trafficking to arms running. Illegal immigration thus helps add to our existing problems with drugs, gangs, and guns.
Finally, studies of the incarcerated population are all over the lot. Some show illegal aliens commit relatively more murders and sex crimes.
You attempt to whitewash the dangers of illegal immigration by distorting the meaning of statistics and drawing incorrect inferences from the data. But it is very unconvincing. Every mugging, drug sale, rape and murder committed by an illegal alien is a crime that could have been prevented by stopping illegal immigration. We can’t kick out home grown criminals, but we can sure do a better job securing the border and thus stop adding to the number of criminals on our soil.