Just for starters, "ethnic groups" don't claim anything at all. You may have seen some, or even a large group of people who you perceive as ethnically similar using some public method to express some opinion- they do not speak for all members of said "ethnic group", if that is indeed what they are, and assuming that they do is folly.

But more importantly, I don't think it would settle anything at all.

The truth is, yours is an old and demonstrably false argument. A study of crime would (and in fact, have) very quickly ascertain that it's cause is multifactorial, no one factor, such as ethnic background, can be any sort of predictor for criminality. There are numerous theories as to what drives criminality, like those advanced by Durkheim, Merton, and others- no modern theory looks at crime within the scope of one element which you suggest, "would help to settle the matter one way or the other."

What attempting to ascribe an ethnic congruity to something negative does is satisfy our desire to feel like we can quickly identify and solve a problem- it is what I call, "intellectual laziness", because it simplifies that which isn't simple and elicits satisfaction in having done so.

This is an exceptionally dangerous road to travel- the illusion of being informed makes it much harder to convince someone they are wrong, rather than when you start with someone who knows they don't know.

It's not a question of it being politically correct or not- it's about making people understand that there are no simple answers to complex problems. Framing it as a matter of "oh it's impolite to bring this up" ignores the truth of the matter.