We have "police must identify themselves" baked into the public consciousness to the level that the drunkest guy in the Saturday night holding cells still manages to belt out "What's yer badge number?"
Accountability is part of it, but I think the bigger part of that is how it terrorizes people to be (or see others) swept up by a gang of unidentified thugs.
It's all interconnected. Getting grabbed by a gang of masked thugs is terrifying because you have no idea what is going to happen to you.
When you're grabbed by uniformed officers who identify themselves, you have some foreknowledge of the process you're entering into. The process is not perfect and it can still harm you greatly, but there's rules and at least some of them are likely to be followed. There's accountability, and that accountability gives you some assurance.
You can't make those assumptions about a gang of masked thugs.
ICE is scared of accountability.