Problems with crime rate numbers is they don’t habitually account for citizenship and crimes can go unreported for fear of legal repercussions.
Economic effect involves numerous competing variables that are extremely difficult to account for. Also, a person may reasonably find fault on the basis of negative impact in one area, notwithstanding the overall impact.
No doubt we can both compile facts and links to support one argument or the other, but we can’t pretend there is a pat answer.
Some studies on the matter are pretty comprehensive, and there are quite a lot of them. It’s better to look at the studies that exist (keeping their limitations in mind) than to imagine that for every existing study, there must be an equally valid and politically opposite study somewhere else that you haven’t seen. That assumption may turn out to be as safe for crime statistics as it is for global warming. This is how researchers get scapegoated – people assume because science is neutral that if all the research answers a political question one way and none of it answers it a different way, all of the scientists involved must be politically biased. When what it really means is that this particular political question is pretty easy to answer and we can spend our efforts trying to answer one of the many harder ones.
This is a pretty comprehensive and recent study:
https://onlinelibrary.wiley.com/doi/full/10.1111/1745-9125.12175
You are correct that crimes absolutely do go unreported when the victim is undocumented, which is the whole reason sanctuary cities improve public safety. The extra undocumented-specific disincentive for reporting is exactly the same as the extra undocumented-specific disincentive for criminal behavior – fear of deportation.
Overall, the NCVS results demonstrate that the findings reported in the main analysis are more likely reflective of less crime, not just less reporting. Though it remains possible that the NCVS results are driven by nonresponse bias among undocumented immigrants, several points suggest this is unlikely to be the case. First, this would not explain the homicide findings, which preclude reporting omissions, and homicide rates tend to parallel trends in overall violent crime substantially (the correlation between murder and the NCVS robbery rate in our data is .83). Second, if nonresponses were driving the NCVS results, we might expect to see substantial differences in nonresponse rates for racial/ethnic groups more likely to be undocumented. But we find little evidence for this.
Not saying I disagree that there are hard aspects to the subject of immigration, and areas where the data isn’t clear, and I honestly probably agree with you on more than either of us would expect. But this crime rate stuff does appear to be very much like global warming. It all points one way.