I have some ideas about why the last released Antibody data from NYC was in mid April. I'm pretty sure it's to do with politics and not science. Herd immunity is a bad look for a politician. But that is pure speculation.
That crossed my mind as well, but if this were the case, surely a member of the opposing party would fund such a study. Given that this also hasn't happened, I wonder if there's another reason. Is it not as simple as paying 1K random ppl $100 to come in and take a test?