Organizations build cultures over time and culture is powerful. There is a reason for example, that the Red Army was a target and not a tool of repression.
DHS and ICE are uniquely suited for being tools of abuse.
We are not that far away in time from when FBI agents only wore white dress shirts. Hoover certainly abused liberties, but he built the bureau into one of the most trusted and elite institutions in America. You cannot imagine Hoover’s G-Men wearing balaclavas and disappearing people. Subsequent reforms made it hard for them to return to freelancing. It attracts a better class of person with more education and more options and they tell you your job is to catch spies and terrorists and the worst criminals. They are told that to do their job effectively they must be trusted by everyone but the real baddies. They believe it, mostly.
The CIA cannot be effectively and widely used against regular Americans. The people they hire and the skills they recruit for are completely unsuited to doing something like listening to opposition politicians or infiltrating domestic gatherings. Their people would be angry, insulted, and resentful if you even asked. Not even on (only) moral grounds but simply because they’d be bored and see it as beneath them.
DEA and ATF are cowboys who deal with a lower class of criminal, who often are immediate and urgent threats. Adrenaline junkies who want to kick down doors and exchange fire (or at least they imagine they are). Again— nothing would be more insulting to them than to ask them to go put cuffs on a fucking mayor who is angry about a new jail.
DHS is new and has no real culture and is a hodgepodge of weird toys. ICE is already conditioned to arrest people who are not really dangerous and whose crime is really just procedural and administrative. They are comfortable rounding people up with a standard of evidence much lower than for a real court. They are conditioned (unlike the FBI) to go into communities and be feared and distrusted even by people who aren’t doing anything wrong. They are a large force present across the country. They are perfect for this stuff.