Do you know how low NY's turnouts have been historically? Answer: Shamefully low...
NYC turnout has historically been even lower than that of the State at large. I have not seen very solid data as yet but it sort of looks like this time there was maybe 12% Democratic turnout in the City as compared to the previous 11%. It's still indicative of large problems and a lack of voter trust.
I live in Oregon, we are also a closed Primary. We consistently have more than twice the turnout NY manages. That's something NY should not be content with at all. It's also not just in Primaries that NY fails to vote, it's in local elections and every sort of cycle of election. Those who run for city offices are concerned because 8.5 million people with a million voting for the winner is not much of a mandate and it becomes hard to campaign to that needle in a haystack, that on person in eight who is paying attention to the candidates.
NY's low participation rates are contrasted with their registration rates which are really good. NYers register but rarely follow through by voting and those who vote do not always do so consistently. That indicates that the problems lie in election day issues.