I feel like you're not really disagreeing with me. With regard to New York City, from what I can see new cases peaked at the same time there as they did in the state as a whole:
These charts show COVID-19's growth in New York City and beyond.
gothamist.com
And though the numbers fluctuate, there are still hundreds of new cases daily.
By herd immunity, I mean the point at which enough of the population is immune that the virus will die off, irrespective of our behaviour. Which is probably at 60%-70% immunity. I totally agree that before that happens the rate at which new cases are increasing (rate of acceleration) will decrease. But they still will be accelerating! The claim I am addressing is not that having say 25% of NYC infected did nothing to slow the transmission rate. Obviously it did. The claim is that the virus has
already peaked or, burnt itself out or whatever in NYC, and the people there can just go back to living their lives. (When in reality believing that requires a belief in an invisible immunity not seen on the antibody tests. Which
may exist but is invisible precisely because we lack conclusive evidence for it!)
So if R0 was 2.39 say and R is now 1.79 taking into account new immunity, then it will still spread rapidly if we allow it. And to me saying "well everything was fine when we had the lockdown so we don't need to worry" is like calling the fire service when your house is on fire and then afterwards thinking "well, my house didn't burn down so why did I call those people?".