The police have been arresting the wrong person forever. It's much, much, much easier to determine if a person is a legally allowed to be here, than it is to solve a crime.
So what if ICE arrests the wrong person. They'll immediately be released when they show a legal reason to be here.
It's a 1,000 times harder to prove innocence of a non-immigration related crime. Innocent people have been executed.
It's all a tragedy but we don't live in a perfect world. So if an ICE agent accidentally arrests a legal citizen, green card holder, etc. then at least there's no threat of them being executed or being sent to prison for many years. They just have to show a valid ID and the problem is solved.