Not really - we're talking about holding someone (and therefore being responsible for their food, safety, possibly healthcare) until the relevant agency collects them.
Even for mere notification, there's nothing obstructive about refusing, even if there was a prior arrangement[0]. Any cooperation would have been voluntary, and the practice and policy of the administration has changed in a way that adversely affects essential city services if they were to continue to cooperate, so that voluntary arrangement would have been terminated.
> _required_
No citizen is required to make themselves known to their state government either. I'm free to go to NYC tomorrow, rent a room for cash, get a metro card, and tell NYS nothing at all, until I earn enough money to necessitate a tax return and have to give them an SSN or ITIN.
Disaster planning etc. is the responsibility of the demographers and statisticians, at least until the the census rolls around, and they're not particularly interested in identity
> expensive
While I threw that in, I do think the cost concerns are secondary to the overall alignment of incentives. Cities have to work for everyone that lives there; without control over the immigration status of their residents (nor any implication that cities _should_ have that control) cities are better off abstaining from questions of immigration status entirely.
[0]: which there wasn't