Why do cities like San Francisco want to keep assassins in the US?
What they do want is for immigrants to not fear deportation, so they want to make a stand that they'll fight immigration enforcement every step of the way. Hence why they'll get involved with these kinds of lawsuits. Even if ICE purely deported only people who committed crimes other than illegal entry or overstaying a visa; you'd still have plenty of immigrants afraid of all law enforcement. Yes, even the legal ones; nobody wants to have to show their papers on pain of having their life uprooted, even if they have those papers.
I don't know exactly what lawsuits SF is filing, but I'm going to assume the actual legal argumentation is less "let the assassains go free" and more "assassains should serve time in American prisons rather than being deported to Mexico where they'll likely escape and reoffend".
https://jacquelinestevens.org/US-Unlawfully-Detaining.Steven...
1. Due to their being no real central database, it's hard for physical persons in the US to prove their identity and consequently their citizenship status.
2. There are a lot of illegal immigrants in the US.
3. There are a lot of illegal immigrants in the US that have lived here for a long time so the "legality" of their status is muddied. This then makes the whole debate around this more about "what is right" and the emotions involved, instead of what the laws say.