I don't know how this misinformation started spreading but I'm pretty sure 20% is nowhere near enough for herd immunity and I have not seen anything authoritative to the contrary. Barring something compelling to the contrary I see no reason to believe that the disease couldn't spike in NYC again.
There is no compelling evidence proving that the disease cannot spike in NYC.
There are small hints that it MIGHT not be possible. The antibody tests measured the infection rate around April 15 or so, the number should be higher now. Second, there is some evidence that a percentage of people don't develop antibodies (only T cells) but are immune. Finally, we don't really know what is required for herd immunity.
None of this is to say you are wrong, just why it MIGHT be possible that NYC cannot have a second spike.
The point is that if the disease spreads so quickly, and our best evidence from months ago is that 20% of the city was infected, it stands to reason that much more of the city was infected than 20%.
How much more is up for debate. A competent government would be regularly conducting these surveys and publishing the results.
We have been more open, with many protests, streets full of open air bars, etc. for months.
I would bet $100 that NYC, if we could do a full antibody and t-cell assay, would show the majority of the population was infected.
Furthermore, I would submit that R0 as a crude instrument ignores network effects. I'd wager anyone who is a "super spreader" in NYC has been infected at this point.
Some papers have suggested a 20% herd immunity threshold taking into account the network effects. I doubt it's that low, but it is an important factor to consider.
