So now they have not only to determine a person is an illegal alien; on top of that, you want them to somehow determine who is "heinous" and who is "good"? It seems a lot more work, considering the fact that there's no objective scale for "being heinous" (what do you do? You ask their friends?) but there's a reasonably objective way of telling if a person is illegaly residing in US or not.
There is a pretty reasonable way to determine if someone is "heinous" or not, committing a violent crime and being found guilty of it. And if going through a criminal justice system is "too much work", then I'm got news for you about who that's going to be applying to next...