Unlawful presence (being “an illegal”) is a civil matter, and not a crime.US legal system seems to disagree with you. http://www.alllaw.com/articles/nolo/us-immigration/crime-ent... https://fas.org/sgp/crs/misc/RL33351.pdf
It is true that some of the illegal immigrants (e.g. those overstaying visas) may not be guilty of criminal infractions, but most of the illegal border crossers are. As you can see, this question has little to do with ICE as these conditions are written in law, not ICE policies.
Here’s an (old) NYT oped as an example
NYT is not exactly a neutral arbiter of correct word usage, especially in highly politicized matter in which NYT is fully engaged. Additionally, if you do read the article, right from the start it points out that the change from criminal handling to civil is a target of a future reform, not a current state of affairs:
A bedrock premise of smart immigration reform is the sharp distinction it draws between criminal aliens and Americans-in-waiting. While it acknowledges that illegal immigrants need to get right with the law, it treats illegal status as a civil matter to be resolved by the machinery of naturalization, not by the police and prisons.
Nobody would need a "reform" if the above would already be the case.
In any case, ICE has no power to decide any of these matters, beyond very narrow band of operative focus (i.e. how to allocate prosecutorial and prevention resources, etc.) - if something is criminal, ICE can not "decriminalize" it, and if something is not, ICE can not "criminalize" it. That's why the very article you quoted talks about "bills" - i.e. legislative actions - that can do exactly that.