I don't believe this will have much of a net effect on vaccination rate, I believe it will disproportionately negatively impact poor and minority populations in NYC who already have a bad/mistrustful relationship with health care and government, and it is obviously a huge new governmental intrusion into our daily lives. It might well lead to anger and violence (as similar moves have across Europe).
These are my opinions, but I think the strongest arguments against it are facts: if you are fully vaccinated, you are at essentially no risk of serious illness from SARS-CoV2. And literally anyone who wants a vaccine can get one. Those who choose not to get vaccinated are making a risk calculation; they are making a choice.
This policy comes from an almost hysterical fixation on "cases", which are not a metric of any meaning. SARS-CoV2 is not going away. We should be reacting rationally to rates of hospitalization and deaths -- and right now, those are barely changed in NYC, thanks to the very high vaccination rate amongst the vulnerable population:
https://www1.nyc.gov/site/doh/covid/covid-19-data-trends.pag...
One can certainly argue that there exist small groups of people for whom the vaccine is not perfect protection. This is true, but it's no different than all other viruses, which have threatened immunocompromised people forever. We have never before justified such intrusive government policies based on the risks faced by these individuals. So while I empathize with them, this still seems like over-reach to me.