They've stated themselves that they don't have the resources for due process in all of these cases. So, yes. That is precisely what they should do. They can stop putting effort and resources into pointless ones and actually do their job.
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...
